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Contexts have historically been either ignored completely or else
treated as black boxes, as indivisible atoms. About a decade ago, as
part of our work on building the large Cyc(r) knowledge base of human
common sense and common knowledge, our group began to study and
harness the internal structure of that "atom". Each context was said
to have assumptions and content; there was a theory of importing
assertions across contexts; contexts were fully reified first-class
terms in the CycL representation language; they were partially ordered
by specialization to control visibility and access to content; and so
on. That 1989-91 work turned out to be inadequate: it was too
expensive to do nontrivial lifting (importing); to explicate the
assumptions of each context; and to place each assertion/query into
the proper context.
Over the last few years, as the number of Cyc contexts grew into the
thousands, we gained a better understanding of the problem - and a
possible solution has emerged. There is a finer internal structure to
a context than just those two parts, assumptions and content. There
are a dozen mostly-independent dimensions along which contexts vary;
conversely, each region of that 12-dimensional space implicitly
defines a context. In effect that space is the space of assumptions,
and each assertion can be thought to hold true in some region of that
space. A more advanced calculus of contexts is required to handle
those 12-dimensional constructs, but it should be worth the cost: it
should enable a much more efficient, much more focused sort of
"virtual lifting" of assertions from one context to another, and - by
providing a superstructure that can serve as a principled guide to
orient the working KB builder or peruser - it should make it easier to
specify the proper context in which an assertion (or question) should
be stated.
In this paper, we discuss contexts in general, and delineate the
dimensions of context-space. We introduce specific terminology for
describing points and regions and comparative locations along each
dimension. We then consider what ontological engineering will be like
in that world.
Contents
1 SUMMARY 3
2 THINKING ABOUT CONTEXTS 5
2.1 WE ARE SWADDLED BY AN AETHER OF CONTEXT 5
2.2 CONTEXTS CATALYZE KNOWLEDGE-ENTERING 12
2.3 CONTEXTS CATALYZE EFFICIENT INFERENCING 15
2.4 "LIFTING" (IMPORTING) ASSERTIONS FROM ONE CONTEXT TO ANOTHER 16
2.5 EACH ASSERTION HAS A DOMAIN (CONTEXT) OF APPLICABILITY 19
2.6 THOSE DOMAINS ARE APPROXIMATED BY REGIONS OF AN N-DIMENSIONAL SPACE 20
2.7 THE TOP 12 DIMENSIONS OF CONTEXT-SPACE 24
3 DIMENSION-BY-DIMENSION DISCUSSION 27
3.1 DIMENSION: TIME 27
3.2 DIMENSION: TYPEOFTIME 37
3.3 DIMENSION: GEOLOCATION 39
3.4 DIMENSION: TYPEOFPLACE 44
3.5 DIMENSION: CULTURE (RESTRICTIONS ON THE AGENTTYPE) 47
3.6 DIMENSION: SOPHISTICATION / SECURITY 48
3.7 DIMENSION: TOPIC 51
3.8 DIMENSION: GRANULARITY 54
3.9 DIMENSION: MODALITY / DISPOSITION / EPISTEMOLOGY 57
3.10 DIMENSION: ARGUMENT-PREFERENCE 61
3.11 DIMENSION: JUSTIFICATION 62
3.12 DIMENSION: LET'S (AND MISC. DOMAIN ASSUMPTIONS) 63
4 LIVING IN THIS 12-DIMENSIONAL WORLD 65
4.1 HOW KE-ING WILL BE DONE, IN THAT WORLD 65
4.2 HOW INFERENCING WILL BE DONE, IN THAT WORLD 69
5 CONCLUSION 71
ACKNOWLEDGEMENTS 74
REFERENCES 74
APPENDIX A: RECAP OF SOME OF THE MAJOR POINTS 75
APPENDIX B: AN ASSERTION ONLY RELIES ON SOME OF THE ASSUMPTIONS 77
1 Summary
Throughout the history of AI (and of software, of science, or for that
matter of practically any human endeavor) contexts have usually been
either ignored completely or else treated as black boxes
[McCarthy&Hayes 69], as indivisible atoms. We talk about "the
context" of a statement, event, etc. without actually ever delving
into what comprises a context. Intuitively, we all understand the
danger of taking things "out of context", since assertions true in one
context might well be false in a different one. And we understand the
potential usefulness and power of contexts, of being in - and
reasoning within - a context:
* Enabling us to ignore 99.999% of our knowledge so we can focus on
"the task at hand"
* Enabling us to be terse and sloppy in our communications and yet
expect our readers/listeners to understand our intent
* Enabling us to accommodate apparently contradictory information, by
partitioning it out to different contexts
This power is not a luxury. During the 1984-1989 time period, as the
Cyc(r) common sense knowledge base [Lenat&Guha 90] grew ever larger,
it became increasingly difficult to shoehorn every fact and rule into
the same flat "world." Finally, in 1989, as Cyc exceeded 100,000
"rules" in size, we found it necessary to introduce an explicit
context mechanism. That is, we divided the KB up into a lattice1 of
hundreds of contexts, placing each Cyc assertion in whichever
context(s) it belonged.
These early Cyc contexts were full-fledged first-class reified (named)
objects. There was a simple theory of "lifting" assertions across
contexts, to import an assertion from one context into another. Each
context was said to consist of 2 parts:
* assumptions: a set of conjuncts to the antecedants of all the rules
in that context
* content: the set of rules/assertions said to hold, or be true in,
that context]
That late-1980's body of work culminated in a PhD thesis for
R. V. Guha, the person who primarily implemented the Cyc context
mechanism [Guha 91], and sparked a rebirth of interest, lively
discussion, and published articles about contexts [McCarthy 93],
[Buvac 96].
Unfortunately, that first foray into contexts turned out to be
inadequate in several ways:
* The cost of lifting was computationally very high, so only trivial
special cases of it were ever permitted.
* Partly because of that restriction, even when reified contexts were
identified there was little short-term payoff in painstakingly
explicating their assumptions. Not surprisingly, then, very little
such assumption-articulating work was ever done.
* Many of the problems familiar to programming language "packages"
veterans recurred; e.g., asserting P=>Q in one context C1 and
asserting P in a different context C2, and failing to have Q
concluded in some asking context C3 because one or both of the
assertions were not importable into the asking context C3.
* Related to that previous point was the difficulty of deciding in
what context an assertion belonged, or deciding from what point of
view (context) an ASK was being made.
Over the last few years, we have gained a better understanding of the
problem - and a possible solution has emerged. To wit:
There is a finer internal structure to a context than just those two
aforementioned parts, assumptions and content. There are a dozen
mostly-independent dimensions along which contexts vary (Absolute
Time, Type of Time, Absolute Place, Type of Place, Culture,
Sophistication/Security, Granularity, Epistemology,
Argument-Preference, Topic, Justification, and Anthropacity.)
Conversely, each region of that 12-dimensional space implicitly
defines a context.
In effect that space is the space of assumptions, and each assertion
can be thought to hold true in some region of that space.
There is also some finer structure associated with the content of a
context, such as whether the assertion holds somewhere in (versus
everywhere in) that context.
There is also some finer structure to each of the 12 dimensions; many
of them are really a bundle of somewhat-mutually-dependent
finer-grained dimensions; e.g., the Epistemology dimension encompasses
several related dimensions such as Modality (belief versus expectation
versus desirability versus intention versus knowledge) and Disposition
(if x is saying something untrue to y, is this untruth being
communicated as a lie, an error, a joke, a simplification, etc.?)
A much larger calculus of contexts is required to handle 12- versus
1-dimensional constructs, but it should be worth the cost: it should
enable a much more efficient, much more focused sort of lifting of
assertions from one context to another; and it should make it easier
to place a rule or fact (or question) in the proper context.
In the next section, we discuss contexts in general, and then, in the
12 subsections of Section 3, we treat each of the 12 dimensions of
context-space. We introduce specific terminology for describing
points and regions and comparative locations along each dimension.
Finally, in Section 4, we consider what ontological engineering will
be like in that world.
2 Thinking about Contexts
2.1 We are swaddled by an aether of context
To communicate a thought to another thinking being - be it flesh or
silicon - we must encode it in some representation. We might encode
it in an English sentence, a database, a spreadsheet, a C++ program,
etc.
Figure 1. Communication involves encoding and decoding, each of which
are done in some context.
If you pluck an isolated line of code from a computer program, or an
isolated sentence from a book, or an isolated cell from a spreadsheet,
it will likely lose some or all of its meaning. I.e., if you show it
- "out of context" - to someone else, they will likely miss some or
all of its intended significance.
Thus, much of the meaning of a represented piece of information
derives from the context in which the information is encoded and
decoded. This can be a tremendous advantage. To the extent that the
two thinking beings are sharing a common rich context, they may
utilize terse signals to communicate complex thoughts. For example:
* One member of an old married couple inhales a certain way, or blinks
a certain way, and their spouse knows they want to go home now.
* Three lights are lit in a church steeple, and Paul Revere knows that
the British are coming both by land and by sea.
* Each technical field develops its own jargon, notation, and
acronyms, making it difficult for a nonspecialist to decipher texts
in that field.
In a more common, but scarcely less powerful, case, an author employs
a pronoun or an ambiguous noun, and the reader disambiguates it
effortlessly. E.g., if someone writes (or utters) a sentence like
"Fred told the waiter he wanted some chips" the reader (or listener)
would be expected to infer many things. To cite just a few of them:
* Fred wants potato chips, not wood chips, cow chips, bone chips, etc.
* There's no particular set of chips that he wants.
* Fred and the waiter were a few feet apart at the time.
* This telling event took place in a restaurant.
* Fred was a customer dining there at that time.
* The waiter was at work there, waiting on Fred at that time.
* Fred will start eating the chips very shortly after he gets them.
* Fred wants and expects the chips in the next few minutes.
* Fred wants and expects the waiter to bring him the chips.
* Fred wants and expects a single portion (1-5 oz, 5-25 chips)
* Fred and the waiter speak the same language.
* Fred accomplished this by speaking words to the waiter.
* Fred might have said "I want chips", or "Chips", or even "Okay"
* Fred assumes the waiter knows/infers all the above things as well.
* Fred and the waiter were a few feet apart at the time.
* Fred and the waiter are both human beings.
* Fred is old enough to talk (2+ years of age).
* The waiter is old enough to work (4+ years, probably 15+)
* This took place after the date of invention of potato chips (1853)
* "he" means Fred. I.e., it's Fred who wants the chips, not the waiter.
Etc.
We human beings all get by, today, in the real world, speaking and
writing such terse, syntactically ambiguous utterances - such as Fred
saying "I want chips" or, in response to a question from the waiter,
possibly just saying "Okay" - because we all draw on the same seven
elements of shared context:
1. The content of the previous sentences that have just gone by, in
the dialogue.
2. The form of the previous sentences (word choices, sentence
structure, tone, etc.)
3. the underlying substrate of general real-world2 knowledge that we
assume practically everyone knows. In modern America, this
encompasses recent history and current affairs, everyday physics,
"household" chemistry, famous books and movies and songs and ads,
famous people, nutrition, addition, weather, etc., etc.
4. The underlying substrate of common sense "rules of thumb" largely
derived from shared experiences (dating, driving, dining,
daydreaming, etc.) and human cognitive economies/limitations
(misremembering, misunderstanding, etc.), and shared modes of
reasoning both high (induction, intuition, inspiration, incubation)
and low (modus ponens, dialectic argument, superficial analogy,
pigeon-holing, etc.)
5. The current short-term real-world2 situation/problem/task/environs3
that the speaker [or author] and listener [or reader] are in, or
are talking about, and their respective roles in that
situation/task/etc., and what each presumes the short-term goals of
the other to be in that conversation.
6. The long-term background/credentials/occupation/role of each party
- at least those that the other party is aware of or, more
importantly, believes to be true.
7. The history of any memorable experiences they shared together (and
the roles they played in those events), any memorable4 prior
conversations they had with each other.
This sharing of context enables extraordinary degrees of ambiguity and
metonymy to be injected by the author/speaker and tolerated by the
reader/listener. For example, Figures 2a-2e, on the next few pages,
contain five sentences from this afternoon's (1/28/98) USA Today. In
each of those five figures, we point out the uses of context. The
context enables the sentences to be relatively terse and syntactically
ambiguous. The sentence s then becomes part of the context - a new
skin on the onion - enabling subsequent sentences to be even more
terse. So in each case (Figures 2a-2e), the context has two different
effects:
* It forestalls the need to say additional things in (or near) that
sentence s - things which the author expects the reader to already
know or to infer for themselves based on this sentence (and
preceding ones).
* It enables the next few sentences to immediately address the
questions that this sentence s raises. I.e., sentence s passes into
the context, after it's read. It becomes part of the context,
thereby enabling the next sentences to be even terser and even more
syntactically ambiguous.
This paper focuses primarily on shared aspects 3 & 4: the common body
of real-world knowledge and common sense that each person assumes that
"everyone" else already has, about the world. For example :
* you should carry a glass of water open-end-up;
* the USA is a big country;
* every animal has two parents, a female mother and a male father;
* if something is true for all people/cars/dates/..., it's true for
any particular one; etc.
That many of these are simplifications or misconceptions is
irrelevant; what matters is the universality of the agreement, not the
truth or accuracy of the information. After all, there can be, and
are, other contexts that hold that more precise but less widely known
model of that bit of the world.
The other five aspects of shared context (1, 2, 5, 6, 7) are more
properly part of a theory of natural language conversation and
dialogue, and will be dealt with - by us and by Cyc - separately.
Figure 2: Context in a few typical sentences from the 1/28/98 USA Today
Fig. 2a.: "Monica Lewinsky's former lover says she is untruthful."
To whom does the pronoun "she" refer: to Monica or to the former lover?
Does the person claim that Monica always lies, or just sometimes?
What sorts of things is she unlikely to lie about (e.g., her name, her
gender, her home planet, the date, etc.)?
Might a former lover have a grudge or bias against Monica?
Might such a person have some privileged inside knowledge about her?
Is the former lover actually claiming to know that Monica is currently
lying about (the nonexistence of) that particular affair with Clinton,
or just that in the past Monica has lied?
Of all the things that Monica said, which specific thing is this
statement actually suggesting that the reader alter their confidence
in? [Answer: Monica's January 27, 1998 claim to the press - later
retracted - that she did not have sex with Bill Clinton in the White
House.]
Once this sentence is stated, in the article, it becomes part of the
context of the article. The next sentence might answer questions,
tersely, that this one raises. E.g., "However, their separation was
not amicable."
How would the meaning change if "says" had been "admits"? "claims"?
Fig. 2b: "Claris will concentrate on its FileMaker Pro
database software, changing its name to FileMaker."
Consider that first "its". Is Claris renaming an entire product line,
or just one particular copy of a program? Obviously the whole product
line.
Consider the second "its". Is FileMaker the new name for FileMaker Pro or for Claris?
What is likely to follow this sentence? Probably some sort of history and rationale.
Fig. 2c: "College hoops are looking for new faces to carry the game,
as stars leave early for the NBA."
Metaphors are packed into practically every word and phrase in that
sentence. From the wording and/or from prior knowledge, the reader is
expected to infer:
* Was the phenomenon being described always so prevalent?
* Why do the stars leave college early?
* Why do the NBA teams lure them away?
* Why do college teams mind this?
* What will the stars be doing at/for the NBA?
This sentence also sets a strong context; the reader now is ready for
the next sentences to address: Which colleges? Which NBA teams? Which
notable stars? How much money?
Notice that the reader is expected to know what the NBA is, and a fair
amount about basketball in late 20th century America. Think how
baffling that sentence would be to someone 100, or even 50 years ago,
even if the "NBA" acronym were spelled out.
Fig. 2d: "Stay on top of the latest hurricanes and tropical storms in
the Atlantic and Pacific basins using the following links."
The writer assumes the reader will infer the answer to questions like:
* Is this literally, physically "on top"?
* Does this only promise things about the past storms, or about future
ones too?
* Does a storm have to span both Atlantic and Pacific basins to be
covered?
* How does a reader use the links? Do they have to use them all?
* To stay on top, do they have to use the links once or more than
once?
By contrast, there are some less obvious questions that might be
explicitly talked about, in the next few sentences in the article,
such as:
* How often is each linked information source updated?
* How often is the set of links themselves reviewed and updated?
* What the source (and reliability) of the links?
The next sentence can be even terser, as a result, if it answers one
of those questions. E.g., "They change each hour, on the hour",
meaning the linked information gets updated then.
Fig. 2e: "U.S. air fatalities fell in 1997."
Since "fatality" can refer to the deceased person, this sentence could
just be stating the obvious (i.e., that's why those people died: they
fell), but that is unlikely for two reasons:
* Good versus bad taste in making jokes about death
* All readers of the newspaper are expected to already know that
that's generally what happens when an airplane crashes - that's how
and why those people died
So presumably, the sentence is talking about the rate of air
fatalities per year, which number apparently was lower for the year
1997 than for 1996. This raises several questions for which the
answer is not obvious, however, such as:
* Is that statistic for U.S. air carriers, or for American passengers
on all carriers?
* How much lower is it?
* Why was it lower?
* What was the trend in pre-1996 years?
Because of this, the reader is half-expecting to have some of those
questions answered in the next few sentences of the article. Because
of that expectation, the author can be even more terse. E.g., the next
sentence might be something like: "They fluctuate wildly", meaning
that this statistic fluctuates a lot from year to year.
Summary of section 2.1: In 1989 we added a context mechanism to Cyc.
Each context had its own content (set of assertions) and set of
assumptions (some explicit and some as-of-yet unstated.) This
provided some relief for knowledge-entering and for efficient
reasoning - but not enough. After we examine what worked out as part
of that early context mechanism (in section 2.2 and 2.3), we'll turn
to why and how we're changing it.
2.2
Contexts catalyze knowledge-entering
When we write an assertion P - for example, P999: "If it's raining
outside, carry an umbrella" - there are certain circumstances in which
it applies (is a good idea, is valid, etc.) and otherwise it doesn't
apply (is a bad idea, is invalid, etc.) You can think of those
"applicability circumstances" as a set of tests one could conjoin onto
the antecedent of P.5,6
* Some of these tests will already be explicitly part of P, namely
whatever was already considered the antecedent of P. E.g., in the
case of P999 ("If it's raining outside, carry an umbrella"), there
is one test of this sort: the condition that it be raining outside.
* Some tests will be implicit but are so
essential/common/fundamental/... that they are used unconsciously.
These tests may be revealed by introspection, by having the system
get the wrong parses to sentences, or by getting the wrong answers
to questions posed to it. A few of those tests to add to assertion
P999 are collected together in Figure 2f, on the next page. E.g.,
the test that the listener/reader is not going to have both their
arms full. Before you turn the page, take a moment to introspect on
what you think some of the other tests are; there are probably more
of them than you might expect. At any given moment, one has the
illusion of having found them all. This is akin to programmers
believing they've found the last bug in their code.
* These conditions are not likely to come to mind right away, and are
certainly not worth stating over and over again, so it's good to
have a more global way to write, store, and add to them (the
assumptions of a context), rather than having them repeated over and
over again for each member of a large set of assertions. Skipping
these common assumptions (until and unless a problem is caused by
skipping them) greatly simplifies and speeds up the process of
KE-ing (knowledge entering - the process of codifying and
formalizing a set of axioms, rules, etc.)
* In some cases, you won't know what exactly the assumptions are, even
after you spend time and effort trying to ferret them out, but you
may still know that some set of assertions all make more or less the
same assumptions. You could then clump those assertions together
into a context, and provide at least an informal comment explaining
the sense of what the context is meant to capture. [E.g., "dining
in a restaurant", or "War and Peace", or "what Egypt believes the
USA wants Egypt and Israel to agree to".] Most computer programs
that have ever been written fall into this category; the modules of
the computer program share a set of never-explicated assumptions in
common with each other and, hopefully, in common with the user of
the application program.
Figure 2f. Some implicit assumptions made by the innocuous- looking
rule P999: "If it's raining outside, carry an umbrella."
* the performer is a human being,
* the performer is sane,
* the performer can carry an umbrella; thus:
* the performer is not a baby,
* the performer is not quadriplegic,
* the performer is not dead,
* the performer is going to go outdoors now/soon,
* their actions permit them a free hand (e.g., not wheelbarrowing)
* their actions wouldn't be unduly hampered by it (e.g.,
marathon-running)
* the wind outside is not too fierce (e.g., hurricane strength)
* the time period of the action is after the invention of the umbrella
* the culture is one that uses umbrellas as a rain- (not just
sun-)protection device,
* the performer has access to an umbrella; thus:
* not too destitute,
* not someone who lives where it practically never rains,
* not somewhere such as a movie theater where it's too late to take an
umbrella if they hadn't already done so on their way to the place,
earlier
* the performer is going to be unsheltered for some period of time,
while outside,
* the more waterproof their clothing, the longer that time period
* the gentler the rain, the longer that time period
* the warmer the air, the longer that time period
* the umbrella will be used practically the whole time unsheltered
* in the air (i.e., not outdoors scuba-diving, or swimming, etc.)
* the rain is merely annoying; thus:
* not ammonia rain on Venus, radioactive post-apocalyptic rain
* not biblical (Noah's-ark-sized, or frogs/blood as rained on Pharaoh)
* not a hydrophobic person, gingerbread man, etc.,
* not a hydrophilic person, Gene Kelley in love, etc.
For the past nine years, we've been carving the Cyc KB up into a set
of "contexts" or "microtheories." Has it reduced the time needed to
enter knowledge into the knowledge base? Has it been enough? Those
questions have different answers. As for the first question - has the
context mechanism actually sped up knowledge-entering? - the answer is
Yes, it has had two positive effects:
1. Assertions (facts, rules, etc.) entered into a specialized context
tended to be more terse and simpler in form than if they had been
entered into one flat KB.
2. There's a good chance that some similar and relevant assertions
will be close at hand, in that same (or nearby) context, which
someone can copy&edit. But turning to the second question - is
this speedup in the rate of ontologizing sufficient? - the answer
is No, the gains have been undermined and offset by this cost:
3. It is distracting and time-consuming for the knowledge enterer to
select (or, even worse, create) precisely the right context each
time he/she enters a new piece of domain knowledge. And it can't
be skipped: doing a slipshod job of placing each new assertion just
leads to bugs (wrong answers, failure to apply relevant knowledge,
etc.) and thence a large amount of "debugging" that must go on -
i.e., where a "wrong answer" turns out to be due to someone simply
having placed an assertion into the wrong context. Or, just as bad,
the knowledge enterer ignores the context mechanism and the result
is a small number of enormous contexts.
So the challenge is to find a good intermediate-granularity carving of
the KB into contexts: too coarse-grained is like having no contexts at
all: rules are huge and difficult to debug too fine-grained makes it
hard to find the right context for a new piece of knowledge
This subsection has focused on how contexts can speed up KE-ing
(entering knowledge into the KB: browsing, editing, composing new
rules, creating new terms, debugging, etc.) The next subsection
addresses the impact of contexts on speeding up the inference engine -
the automated reasoning processes of Cyc itself.
2.3
Contexts catalyze efficient inferencing
When we are asked to solve a problem P - for example, "Is someone a
priori more likely to be carrying an umbrella open or closed, if it's
raining hard?" - there is some information which is (likely to be)
more relevant than other information. In this case, the purpose and
operation of umbrellas is more relevant than the numbers of legs a
spider has, or the date that Julius Caesar died. To make the
inference as efficient and sensible7 as possible, heuristics are
brought to bear. Here are two such special-purpose guidance
mechanisms that Cyc employs:
1. Some of those heuristics are compiled into a set of so-called
heuristic-level (HL) modules; they mainly increase the efficiency
of the inference process. They recognize special cases - certain
kinds of questions/statements - and when such a case arises the HL
module grabs control and handles that special case by dint of some
customized, optimized data structures and algorithms, rather than
falling back logical deduction (the method of last resort, despite
- because of? - its generality). E.g., answer questions like "Are
any ducks also elk?" by quick tree-searching, not slow
theorem-proving.
2. Some of the heuristics are explicit search-guidance heuristics
invoked by the inference engine; they increase both efficiency and
sensibility5 of the inference process, though it might be
prohibitive to have a huge number of these. These heuristics guide
the inference engine in deciding which sub-problem to tackle next,
at any given moment; what tack to take on that problem; how much
resources (cpu time, elapsed real time, disk space, real-time
queries and email messages sent to human beings) to spend before
giving up or trying a new approach on it, and so on.
Contexts provide a third mechanism Cyc can use to guide inference:
3. Some of the heuristics can be implicitly encoded in a subsetting of
the knowledge base; that is, carving it up into meaningful subsets
such that intra-subset deductions are more likely to be productive
than cross-subset deductions. Each of those subsets is a context.
Thus, carving the KB up into a set of contexts should increase both
the efficiency and sensibility of inference.
If the carving-up of the knowledge base into contexts is too coarse
(an extreme case would be if every assertion were placed into one big
context) that's suboptimal because (i) lots of irrelevant assertions
will be placed in the same context, and (ii) many of the assumptions
will only actually be relied on by a small fraction of the assertions
in that context. If the carving-up of the KB into contexts is too
fine-grained (an extreme case would be if every assertion were placed
in its own separate context) then that's suboptimal due to the high
cost of lots of liftings (importings from one context into another)
that would need to get done. So the challenge is to find a very good
intermediate-granularity. This reinforces the conclusion of Section
2.3, where - to maximize the speed of knowledge entering and KB
building - we also didn't want there to be too coarse- or fine-grained
a carving up of the KB into contexts.
2.4 "Lifting" (Importing) Assertions From One Context to Another
In section 2.2 and 2.3, we saw that contexts may be the key to
drastically faster knowledge-entering and also to drastically faster
inferencing; they have already made the difference between huge
knowledge-based systems existing - namely Cyc - or not existing.
At any given moment, some assumptions will not yet be articulated or
even suspected. When this lack causes some subsequent wrong answer or
behavior, the missing assumption will be painfully clear, and can then
be formalized and added as an explicit assumption. This is a form of
knowledge debugging, in many ways analogous to program debugging. It
is a correctness issue, not just an efficiency issue.
When we lift an axiom P from context C1 into context C2, and use it
there in some inference (with, say, axioms Q, R,... from C2), we need
to ensure that there is no logical inconsistency between the C1
assumptions and the C2 assumptions. If assertions only depend on a
few of their context's assumptions, this will prevent a lot of
otherwise-useful and valid lifting from taking place. So: most (if
not all) of the assertions in a context should actually rely on most
(if not all) of the domainAssumptions of that context. Otherwise we
will get hamstrung by some irrelevant assumption from C1, when we try
to use P outside of C1.
So what do you do if a C1 "assumption" ( only pertains to a sliver of
C1's assertions?
* Split off that sliver as its own little context C1' (and make ( one
of C1''s assumptions)
* Or just conjoin ( to the antecedent of each of those assertions and
leave them in C1.
Here's another way to visualize this situation. Suppose some
assertion P109, e.g., is true in context C1; we want to "import" P109
into context C2 and use it there. What we really want to do is assert
some P109' whose meaning there (in context C2) is more or less the
same as the meaning of P109 in context C1. See Figure 2h.
Sometimes we can just go ahead and assert P109, over into context C2,
with no changes, and it will all work out fine. But often it turns
out that some of C1's assumptions - on which P109 depends - are not
made in C2, and it would be better to conjoin them on the antecedent
of P109. For instance, suppose
C1 = the context of the Heaven's Gate cult beliefs;
A35 = "The Heaven's Gate cult beliefs are right."
C2 = the editorial position of the New York Times in the 1990's
P109 = "The comet Hale-Bopp has a UFO hiding behind it."
One of C1's assumptions is A35: This is a core assumption of the
entire Heaven's Gate microtheory C1. An unsigned New York Times
editorial mentioning P109 would never just assert P109, as though it
were factual, it would say something like "If the Heaven's Gate cult's
beliefs are right, then the comet Hale-Bopp has a UFO hiding behind
it." In other words, the lifted form of the assertion P109 is not
identical to assertion P109 but rather: "If then ."
Assumption A35 was tacked onto the antecedent of P109, because A35 is
not one of the assumptions of C2.8
We can never fully explicate all assumptions underlying the knowledge
we express. No matter how hard we try, some assumptions are bound to
be left implicit. Contexts, just like the real-world situations they
describe, are "rich objects;" i.e., there is an infinity of things one
could say about a context, and of course only a small finite number of
those will ever be explicated.
One extremely special case is when one wants to import an assertion
from a context to a more specific context (e.g., sporting event to
baseball game; or baseball game to professional baseball game.) In
that case, all the domain assumptions are (by default) still satisfied
in the more specialized context, so any assertion can just be imported
(unchanged) from the general context to the more specialized one.
This is still just a default, of course; e.g., there could be an
assertion in the specialized context that contradicts and overrides
it.
A special case of "importing to a more specialized context" is the
case of importing from the BaseKB (the most general context of all).
There should be precious little in the BaseKB, since all of it must be
freely importable - unchanged - to every other context.
A more complicated case arises when a domain assumption has the form
of an implication - i.e., it is some general "if/then rule",
intuitively. For example, suppose one of the assumptions of a
military infantry-combat context (call it MilInfantryCombatMt) is that
people mentioned anywhere in that context are (by default) male:
(domainAssumptions MilInfantryCombatMt
(implies
(isa ?x Person)
(isa ?x MalePerson)))9
And suppose we're lifting an assertion P1 which has a conjunct (isa ?x
Person) in it - that is, in its antecedent or its consequent. Then
the lifted form of P1 in some more gender-neutral context (one which
doesn't assume the bias that people are by default male) should have
that conjunct replaced by (isa ?x MalePerson). For example, consider
a rule in MilInfantryCombatMt like "almost everyone over 30 has a
wife." Suppose this rule happens to be true there - remember, in that
context "everyone" refers to male infantry soldiers. Lifted into a
less gender-biased military context, it would become "almost every man
over 30 has a wife." Lifted into a gender-biased but non-military
context, it would become "almost every infantry soldier over 30 has a
wife." And if the rule were lifted into a context that was neither
gender-biased nor military, then it would become "almost every male
infantry soldier over 30 has a wife."
A related, but even more complicated, case is where there is an
implicit "personhood" of x, either because of other assumptions, or
argument-type constraints, or information lifted from some third
context, etc. In that case, a whole new clause of the form (isa ?x
MalePerson) must be added (to the antecedent of the rule). In our
last example, if the original rule in MilInfantryCombatMt just had the
variable x be universally bound, then when lifted into a context in
which some of the performers were nonhumans (animals, corporations,
etc.) a whole new clause (isa ?x Person) would have to get added.10
In cases where it's not so clear how exactly to insert the old
context's assumption into the assertion being lifted, one can always
fall back on the crude but logically equivalent approach of
conjoining, to the antecedent of the assertion, all the assumptions of
the old context it's being lifted from. E.g., in the case discussed
above, one of the conjuncts that would get added would be (implies
(isa ?x Person) (isa ?x MalePerson)).
2.5 Each assertion has a domain (context) of applicability
So far we've been talking about contexts as though they're the real
objects, and they happen to have (i.e. contain) assertions. There is
an alternate way to view things, a "dual" view, in which assertions
are the real objects, and they happen to have (i.e. hold true in) some
contexts. This section explores and expands that point of view.
Each assertion P is true in some contexts, and false in others. So in
theory you could write down any old random assertion P - for instance,
"Pigs can talk"- and then assert it to Cyc, so long as you thought
about and articulated (to Cyc) the contexts in which P holds - such as
the novel Animal Farm and the movie Babe and the TV show Sesame Street
and various other fictional stories and delusional belief systems.
You'd then eventually make this more parsimonious by finding and
asserting the most general mutually-incommensurable contexts in which
P held.
Letting each assertion define its own unique context is not such a
great idea efficiency-wise, though. As we discussed in Section 2.2.,
finding the right context would then be a nightmare. And for reasons
discussed in Section 2.3, inference would be slower rather than
faster, because of all the lifting that would constantly have to get
done.
The basic idea still is valid, though: when you decide to enter some
new assertion P into the KB, you should think about, and articulate to
Cyc, the (most general) contexts in which P holds.11 It's just that
there should be some faster way to do that than by browsing through a
million contexts and pointing at the right one. Snazzy graphical
browsing interface tools won't by themselves help enough here; after
all, even log 2(1,000,000) is an awful lot of things to go through by
hand every time you enter an assertion.
Similarly, each question Q has an answer (such as one or more sets of
variable bindings) in some contexts, and the answer may vary from
context to context. If the context of the question is unspecified (or
under-specified) then the "answer" could/should really be a set of
pairs. E.g., "What will the weather be like?" has
different answers, depending on who's asking, where they're going, the
time of day they're asking about, the season of the year, etc. Even
the question "Who's president of the USA?" has dozens of answers,
depending on the date for which an answer is sought to that question.
2.6 Those domains are approximated by regions of an n-dimensional space
When we say (ist C P), we mean that P holds in context C. That is,
assertion P is true in context C. But what sort of beast is C? We
can reify a context, and then give that specific name in place of C.
As we discussed above, that would be a bad idea: almost every
assertion in the KB could have its own unique context, even though
only a minuscule fraction of those contexts actually merit their own
names.
On the other hand, we can easily articulate several properties that
separate one context from another: level of granularity, time, place,
topic, etc. These can be thought of as the labels on different
coordinate axes in n dimensions. Then each context is a region of
that n-space.
Point 1: Besides thinking of a context as "a named node in an
ontology12", let's also think of it as being13 "a region in some
n-dimensional space".
Specifying a context therefore entails specifying or locating a point
or region along each of those n dimensions.14 This applies to
asserting some proposition, to asking for an answer to some question,
to asking for a justification, etc.
The old Cyc genlMt predicate is just one simple relationship that can
hold among two contexts; it roughly corresponds to "proper subset-of
(or similar restriction) in some m dimensions, and no change (that is,
equality) in all the other n-m dimensions." Thus, in one situation
genlMt might hold between The1920sUSA and TheTwentiethCenturyUSA - in
this case meaning "is a temporal slice of"; in another situation it
might hold between HumanActivitiesMicrotheory and
AnimalActivitiesMicrotheory, meaning "has a more restricted set of
default actors than"; in another situation it might hold between
NewtonianPhysicsMt and NaivePhysicsMt, meaning "is a more precise and
accurate theory than"; and so on. In many ways, our naiveté in the
early 1990's in having just this one vague genlMt predicate is akin to
the error that other ontologists make when they have just one
a-kind-of relation, instead of distinguishing - as we've done for 15
years - the relations isa (element-of), genls (subset-of), genlPreds
(restriction-of-predicate), partOf, subRegionOf,...
So What's The Big Deal about Point 1? Point 1 sounds rather tame, but
in fact it embodies a highly unorthodox alternative way of looking at
the world; possibly a full-fledged paradigm shift. The three best
analogies that come to mind are these:
Analogy 1: Besides thinking of real world substances as named
substances in a hierarchy (with nodes like wood, chocolate, iron,
silk, etc.), let's also think of each as being a region in some
"chemical-formula-space." A set of just 100 chemical elements then
generates the huge set of formulae for all possible chemical compounds
- plus many impossible ones.
Analogy 2: For those of you trained in physics, another good analogy
is to the way that quarks (with their dimensions of strangeness,
charm, direction, etc.) are an alternative and - even without their
being detectable directly - a much simpler, more organized way of
describing the otherwise tangled plethora of elementary particles that
have been experimentally observed and measured in cloud chambers and
particle accelerators.
Analogy 3: In the mid-1980's a former Stanford Ph.D student of mine,
Paul Cohen, who was by then a University of Massachusetts professor,
came up with the idea that the tens of thousands of relations
(predicates, slots,...) that we see and name and organize might all be
just surface manifestations of "allowed points" in an n-dimensional
matrix, a "slot-space" if you will. The dimensions of that slot-space
are attributes true for some predicates and false for others; e.g.,
transitivity, insensitivity to time's arrow, and so on.
If you have say a dozen such dimensions, and each one has even just a
few different values, that already is a million distinct points in
slot-space: in principle far more than enough to differentiate the
several thousands of slots/predicates/... named in English, and in
Cyc.
Professor Cohen, and his student Cindy Loiselle, and later the Cyc
group and others at MCC (notably Michael Huhns and Larry Stephens),
put this to use doing something astounding: automatically guessing
what the composition of two slots (binary predicates) might be, in
cases where that composition turned out to equal some known
slot. Consider Figure 2i, below. For each dimension d, they analyzed
what the possible d-values could possibly legally be, for the
composition R = p2 o p1, given the d-values for p1 and p2. For
instance, if both p1 and p2 are transitive, then so must be R. This
set of constraints is applied to a particular pair of relations such
as "owns" and "physical-parts", and yields a set of constraints on the
value of R in each dimension. By looking over the set of known
predicates, a very small number of predicates may be consistent with
all those constraints; in this case, e.g., all that might be left as
potentially legal predicates R is the predicate "owns", so the system
can hypothesize that if x owns y, and one of y's physical parts is z,
then x owns z. E.g., if you own a car, then you also own its steering
wheel. Of course this algorithm doesn't always work - there might be
more than one consistent predicate, or the composition might not be
any known predicate at all - but it's like the tap-dancing bear: the
fact it does it at all is amazing. Thus ends Analogy 3.
Criteria for Preferring One Dimension Over Another. The following
sort of utility consideration must ultimately be the criteria for
deciding which "dimensions" we support or don't support:
Utility of a dimension should be measured by:
* success in separating out mutually-irrelevant portions of knowledge
from each other.
* ease of computing the overlap / disjointness of subsections of the
dimension.
* how much they tease apart notorious large KB clumps (e.g.,
HumanActivitiesMt)
* whether the points and regions (especially the extreme ones)
correspond to semantically familiar and important real-world
concepts and considerations
Utility of a dimension should not be measured by:
* how closely it satisfies some arbitrary
philosophical/linguistic/... model
* whether there happens to be an existing English word succinctly
capturing it
* notions of "cleverness", "cleanness", "novelty", "symmetry",
"academic interest"
* the need to have 10 dimensions, or 42, or 666, or any particular
favorite number.
Let's stop and recognize that there will be no true limit to the
number n of dimensions of context-space that one could
identify. Although the general domain assumptions/ relevance/lifting
problem is arbitrarily hard, we are going to use an 80/20 approach to
get the most bang for the buck: There is a small set of n useful,
important categories along which context-space can be crudely
partitioned. The first dozen or so of these dimensions will provide
the maximal utility for the minimal cost. We arrived at the figure of
a dozen dimensions by enumerating a much larger set of dimensions
(over 100), and then clumping together the two most closely related,
again and again, until there were no closely related dimensions any
more.
The Order of Dimensions Matters, and There Can Be Repeated Dimensions
When we have a set of universal and existential quantifiers, the order
matters of course. The same is true when we have a set of dimensional
qualifiers. Thus, e.g., "For all moments during the 1800's, for some
place in each world capital, ..." is different than if those clauses
had been reversed. There is no fixed order in which the dimensions
are evaluated; rather, that order is specified for a context by
(earlierDimension C d1 d2), which defines a partial order of the
dimensions di such as Time, GeoLocation, etc. However, our
expectation is that the order of dimension-constraints will rarely
matter.
We also note that it therefore might happen that some dimension gets
qualified two or more times, presumably at different places in the
layerings of qualifications, above. E.g., ., "For all moments during
the 1800's, for some place in each world capital, sometime on
Christmas eve, P" where the exact time on Christmas eve that P holds
depends on the country. And exactly where, in each capital, depends
on what year during the 1800's it is. Those two temporal
qualifications (year in 1800s, time of day on Christmas eve) can't be
merged; all 3 qualifications need to be there, in that order:
time/place/time.
2.7 The Top 12 Dimensions of Context-Space
Well, okay, but what are the dozen most useful dimensions of
context-space? And what sorts of values are there along each
dimension? Are certain regions of this n-space "special" or
"prohibited"? Are there some facets (attributes, modifiers) for those
values? What about 100 sub-dimensions23 that led to this set of a
dozen "clumps" of dimensions?
The 12 (classes of) dimensions of context-space we will discuss in
Sections 3.1 - 3.12 are:
1. Absolute Time: a particular time interval in which events occur
2. Type Of Time: a non-absolute type of time period, such as "just
after eating"
3. Absolute Place: a particular location where events occur, such as
"Paris"
4. Type Of Place: a non-absolute type of place, such as "in bed"
5. Culture: linguistic, religious, ethnic, age-group, wealth, etc. of
typical actors
6. Sophistication/Security: who already knows this, who could learn
it, etc.
7. Topic/Usage: drilling down into aspects and applications - not
subsets
8. Granularity: phenomena and details which are (and are not) ignored
9. Modality/Disposition/Epistemology: who wants/believes this content
to be true?
10. Argument-Preference: local rules for how to resolve pro-con
argument disputes
11. Justification: are things in this context generally proven,
observed, on faith...
12. Let's: local bindings of variables etc. that hold true in that
context
Point 2: Placing each new assertion P into the ideal context is
expensive today. Idea to speed it up: have it be mostly just
stating/choosing 12 meta-level values.
Point 3: Automated inference over a million-rule KB is expensive
today. Idea to speed it up: localize the search, favoring the content
in same/nearby contexts.
As Point 2 (in the box, above) says, this should speed up
Knowledge-Entering. As Point 3 says, this should also speed up
Inferencing.
Before treating each of the dozen dimensions in detail, let's address
the question of what some also-ran would-be dimensions are, and why
they weren't chosen, and how they'll be handled under the new system.
Non-Dimensions. There are several non-dimensions or
pseudo-dimensions; that is, things that at first glance might appear
to be possible dimensions, but at second glance appear to not be such
after all. E.g., the following phenomena must be handled somehow, we
just suggest that these not be done by trying to tease them out as 8
more dimensions:
* a tag about the probability/certainty/monotonicity of a set of
assertions
* a tag about whether a set of assertions is meant to be run
forward/backward
* a tag about whether typical propositions in some context - which has
some time/place/sophistication/... interval specified, such as
"The1920's" - are claimed to hold throughout that entire interval or
just at some points/subsets of that interval. (Or even worse,
having a "dimension" like this for each of the 12 other dimensions.)
* other tags, similar to the last one, but talking about whether
intervals should be assumed to be open (not including their
endpoints) or closed, solid or disjointed, finite or infinite or
semi-infinite (infinite in one direction only), and so on.
* a specific region of any (valid) dimension
* quoting. This means that we want to represent the fact that #$Lenat
is a Cyc term, and #$Lenat is a person, and yet people are tangible
and Cyc terms aren't. What's the solution? We can use a kind of
quoting operator; so if we write the expression (quote #$Lenat) or
'#$Lenat, that represents the Cyc term #$Lenat (which then in turn
represents the person). Without the quote-mark, #$Lenat is a Cyc
term and represents the person, not the Cyc term.
* physical attributes, such as: Temperature, Pressure, Orientation,
Stability, etc. of the typical objects and events talked about in
this context.
* The level of "anthropacity" of the context, by which we mean what
does it presume that there "is" in the world: a physical universe?
Like ours? People? Human history as we know it? Etc. This can
largely be computed from the various assertions (and assumptions) of
the context. E.g., if assertions talk about I Love Lucy shows then
the world must be pretty close to ours.
The Final 99% of the Dimensions. Specifying values for the most
important dozen dimensions doesn't always fully specify the context,
but it does dramatically cut down on the number of contexts (worth
distinguishing) once you've specified the values for all 12
dimensions. This is analogous to a hashing function, where there
still might be a few input items that hash into the same "bucket", but
if the programmer has done his/her job well, then that's usually not a
problem. In this case, each 12-space region might be considered a
"bucket" of contexts; the contexts in that bucket would organize (via
genlMt and other inter-context relations) into hierarchies. The seven
non-dimension features bulleted above would not be distinguished in
that imagined hash table, even if there were several reified contexts
at one of those terminal buckets.
A note on the "number of buckets": even if we only distinguished ten
points in each dimension, that means that trillions of distinct
context "buckets" would thus be defined. Each context in that bucket
would, presumably, make some additional assumptions that didn't quite
fit along any of the 12 dimensions; e.g., making assumption about the
temperature, or pressure, etc. in which events (talked about in
assertions in that context) transpire. Temperature and Pressure may
not be worthy of being dimensions in their own right, hence
assumptions involving them are stuck on, at the end, as domain
assumptions of that context, after it's been situated into 12-space.
As with hashing, if we do a good job in selecting the top 12
dimensions, then all the rest, the final 99% of the dimensions, won't
matter that often, vis efficient KE-ing and inferencing. So some of
the domain assumptions of a context will now be specified by its
12-space location, and the leftover domain assumptions will be
specified explicitly (when they are known/thought about) as Cyc
formulas which are then the listed domainAssumptions of that context.
The Plan for Sections 3 and 4. In the 12 subsections of Section 3, we
will treat these chosen 12 dimensions one at a time, covering such
topics as:
* the basic idea behind each dimension
* the reasons why it is an important dimension
* examples of extreme and typical points/regions along that dimension
* the new vocabulary of terms (collections, predicates, functions,
individuals, etc.) that we have now in Cyc to handle that dimension.
These are terms are used:
* to specify points on that dimension
* to specify regions of that dimension
* to specify relative positions of points on that dimension
* to specify relationships between regions of that dimension
* our current ideas and plans for future extensions of that
vocabulary, if any
Finally, Section 4 discusses some pragmatic issues about how to thrive
in this more complex 12-dimensional context world - from both a KE-ing
and Inferencing point of view.
3
Dimension-by-Dimension Discussion
3.1 Dimension: Time
Often, one context C1 is separated from another C2 in that the things
true in C1 are true at a different point/region of the timeline than
the things true in C2. E.g., one context might be temporally situated
"during the Crusades", and another might be talking about events
"during the 1990's". Obviously many of the things that are true in
one of those contexts will be flat out false in the other.
So this - Time - will be our first dimension. Each context in Cyc
will have a piece of time associated with it. The assertions that
hold true in that context will be presumed to be occurring during that
piece of time.
What makes this such a great dimension to have is the fact that, in
the real world, causes precede effects by a small (or zero) amount of
time. Whether the action is spilling a glass of water, or fighting a
battle, the objects interacting with each other will generally be
intersecting in time, and their interactions will take place in that
piece of time.
That piece of time can be as simple (e.g., a point, a solid interval)
or as complex (e.g., a series of discontinuous pieces such as "every
second Wednesday morning") as any piece of time in Cyc. It can be
named (e.g., TheYear1956) or not. It can have some significance that
goes beyond being the Time locus of the assertion (e.g., WorldWarII),
or not.
There are a few thorny issues here. For the purpose of this
discussion, let C be a context with Time value t. And let's suppose
that assertions A1, A2,... hold true in C.
3.1.1 Always-True-During vs. Sometimes-True-During
Is A1 true during the entire piece of time t, or just true sometime
during t? Often the answer is pretty clear (e.g., "JFK died on
November 23, 1963" means sometime during that day; "Doug was a
6th-grader on November 23, 1963" means for that entire day).
Sometimes it's not so clear what's meant (e.g., "Jane was married
during the 1980's" - though even in an ambiguous case like this one,
"during the 1980's" means presumably that there is some single
unbroken interval M of time that intersects the 1980-90 decade-long
interval such that Jane was married during that entire interval M.)
3.1.2 Temporal Projection.
Given that assertion A1 holds at a certain time, it's likely to
continue holding for "a while" and it's likely that it had already
been true for "a while." How can Cyc automatically decide how far
into the future/past a certain condition persists? More precisely,
there is a probability or likelihood distribution over time - both
before and after the stated time period in which an assertion is
stated to hold - of whether it was/will be still true.
For example, consider "Billy was in pain when he fell and sprained his
ankle." You know that he probably wasn't in pain just before that,
not even a second before that moment (unless we have some other
argument for why he was); and you know that Billy probably was in pain
10 seconds later. How about 2 minutes later? 20 minutes? 2 hours? 2
days? 2 weeks? 2 months? 2 years? Somewhere along the way, your
answer changed from Yes to Maybe to No (meaning: at least not just
because of this specific accident).
The "proper" way to treat this would be for someone to specify some
sort of distribution in which the likelihood of Billy being in pain
(because of this accident) is zero before the accident occurs, then
discontinuously jumping up to about 100%, and then falling off for a
while until it reaches a near-zero asymptote after a day or two.
This is a dangerous tarpit; we don't want our ontological engineers
sitting around all day agonizing over nuances in probability
distributions - that would be even worse than the mid-1980's bout we
went through of agonizing over numeric certainty factors. So what's
our proposed solution? We present it as Point 4:
Point 4: Each assertion points to one of a handful of persistence
distributions (spike, step, uniform, normal, etc.) and gives a crude
estimate of the parameters of that distribution (e.g., mean and
standard deviation in the case of a normal distribution, or max/min
and overall length in the case of a less regular one).
3.1.3 Relative vs. Absolute time
Much of this Time information will be relative, not absolute. What do
we mean by "relative", here? Let's explain this by considering an
example. Suppose you drop a raw egg on a hard stone floor from a
height of about 6'. What will happen?
* First, for a small period of time thereafter, it will be moving
* downward.
* Then, when it contacts the stone, it will stop moving and start
* breaking
* In less time than it would take me to jump out of the way, the
* contents will spatter out.
* For a short time interval following the splattering, I'll have wet
* egg on my clothes.
The durations and starting/ending times of these various events could
be specified in an absolute sense, by citing a particular duration
(e.g., "0.532 seconds"), or a particular point on the timeline (e.g.,
"14:52:09.003 on Tuesday, October 13, 1998."). But they aren't.
They're specified relative to other events' durations (such as "less
time than it would take me to jump out of the way") and
starting/ending time points (such as "when it contacts the stone.")
These are relative ways of specifying duration and starting/ending
times.
3.1.4 Inferring (e.g., inheriting) those 3 types of meta-level information
So how does Cyc decide whether assertion A1 is true sometimes-during
or always-during the time period of context C1? How does Cyc decide
whether it applies to some particular absolute piece of time, and/or
standing in some relation to some other event or piece of time? How
does Cyc decide how long in the future that assertion will remain
true? To make the task of specifying these three types of meta-level
information much less time-consuming, each of them will almost always
be inferable (i.e., computable) from the predicates and other terms
used in the assertion, and/or be a default attached to the context as
a whole. In rare cases some special meta-level assertion about A1 will
have to be made. A similar tripartite scheme (context-wide unless
predicates-involved unless idiosyncratic-for-that-assertion) applies
to most aspects of most context-space dimensions, not just Time.
Point 5: Most assertions' persistence-distributions are "inherited"
from a single default distribution attached to their context (and, in
turn, even that is typically inherited/inferred); a few assertions get
this overridden by dint of their particular predicates (such as gender
and birthDate) [usually their main predicate] possibly with some
typing of arguments to that predicate.15 And, finally, there is the
very tiny fraction of the KB's assertions that need to have a
manually-entered persistence-distribution. A similar tripartite
scheme (context-wide unless predicates-involved unless
idiosyncratic-for-that-assertion) applies to deciding if it's
sometimes-true-during C1 versus always-true-during C1; etc.
So the ontological engineer will hopefully only rarely have to attend
to the persistence distribution type, and its parameters - for
example, they might need to attend to it explicitly during debugging.
And, during debugging, a good interface might let them modify those
parameters (semi)automatically, by complaining that the truth of a
certain assertion should - or should not - have persisted to a certain
point in time.
That same argument applies to the absolute and relative specification
of the Time interval itself: In most cases, both the duration and
starting/ending times ought to be guessable (semi)automatically by the
system, based on terms used in the assertion. At the least, relative
constraints on the Time value should be inferred from the assertion,
connecting that piece of time to other pieces of time. In the case of
"George Washington wears wooden teeth", e.g., the Time period of the
objective content is during that person's lifetime, and also during
the time period of commercial use of wooden teeth.
Sometimes a piece of time is so simple that it's just a continuous
block of time from some starting point to some ending point. In that
case it can be represented by two numbers, if the absolute endpoints
are known. Sometimes one or both of the endpoints won't be "in" that
piece of time. E.g., the time after 3pm and before 4pm today does not
include either endpoint. Even in less trivial cases, pieces of time
can be naturally partially-ordered by inclusion, and they thereby form
into a lattice.16
Most of the above remarks apply to more dimensions than just Time.
E.g., in a New Jersey context, someone states "Gambling is legal";
does that mean it's legal somewhere in the state, or everywhere in the
state? Does New Jersey include its borders or just the land inside
those borders?
3.1.5 True-in-time versus Relevant-in-time
One final issue to address here is to distinguish "true-in-time-x"
from "relevant-in-time-x". This is a somewhat subtle point, but turns
out to be very important for efficiency reasons - including both
efficiency of knowledge-entering, browsing, and inferencing.
Consider the sentence "Bill Clinton is the President of the USA."
This is true in some contexts (e.g., TheYear1997) and false in other
contexts (e.g., TheYear1900). Now consider the sentence "Bill Clinton
is the President of the USA during 1997." This statement is true for
all time, not just during 1997. In the year 9999 it will still be
true. In 1900 no one knew this fact, but it was still true. It was
largely irrelevant in 1900, in the sense that no one then acted
differently because of it (since no one knew it.)
Thus: Many assertions are strictly speaking true at all times, or for
a wide swatch of the timeline, but are only relevant to some small
sliver(s) of time. This is a strong enough schism that there should
in effect be two Time dimensions, one for truth and one for relevance.
At any moment, P is not true iff (if and only if) not-P is true. But
it is often the case that both P and not-P are irrelevant, at the same
moment.
3.1.6 Temporal Granule Size
Each context has some notion of what it means, in that context, to be
a "moment" of time. Differences in time smaller than that granule
size are just not even talked about in that context. For a track and
field event, it might be 0.01 second; for a macroeconomic theory of
nineteenth century Europe it might be 1 day or even 1 year.
The temporal granule for a context will almost always have a known
duration. It will often have some tie-in to some absolute
calendar-type time. Furthermore, some contexts will have granules of
a few different sizes. E.g., for a New York Stock Exchange context,
the granules might be tied to one trading-day; hence one would be an
8-hour block of time on a non-holiday weekday starting at 9am and
ending at 5pm East Coast time; one would be the 16-hour period between
most trading-days; and one would be the 64-hour period "over the
weekend" between close of business Friday and the market's opening on
Monday morning.
3.1.7 Vocabulary for expressing this in Cyc
Putting the above discussion all together, we have for Time the
following:
-One portion of a context's content is just "true", the rest is both
"true" and "relevant." One portion of a context's content holds
throughout a whole time-interval ti, the rest just holds sometime
during that interval.17 These two binary choices effectively carve
each context up into four discernable regions.18 In Cyc there are 4
functions that connect a context to these 4 more specialized (and
probably non-reified) contexts. See Figure 3a.
(#$Relevant+AlwaysFn C t) = C1 means that the assertions in context
C1 are precisely those assertions that hold in C and which happen to
be both true and relevant throughout the entire temporal extent of the
TemporalThing t.
(#$Relevant+SometimesFn C t) = C2 means that the assertions in context
C2 are precisely those assertions that hold in C and which happen to
be both true and relevant during at least some portion of the temporal
extent of t (a #$TemporalThing.) Note that (for all C and t) (genlMt
(#$Relevant+SometimesFn C t) (#$Relevant+AlwaysFn C t)).
(#$AlwaysFn C t) = C3 means that the assertions in context C3 are
precisely those assertions that hold in C and which hold true
throughout the entire temporal extent of t. Note that (for all C and
t) (#$genlMt (#$AlwaysFn C t) (#$Relevant+AlwaysFn C t))
(#$SometimesFn C t) = C4 means that the assertions in context C4 are
precisely those assertions that hold in C and which are true during at
least some portion of the temporal extent of t. Note that C4 will be
a specMt of C1, C2, C3, above. For some t, C4 = C.
-Another component of each "value along the Time dimension" is the
granule size and, if known, a more absolute calendar-based
characterization of the granules. This indicates how small a piece of
time is before it's considered an indivisible moment. We write
(mtTemporalGranuleSize C t) to indicate that context C has, as such a
granule size, the size of the duration of temporal object t.
If we know not just the right duration, but the particular granules
themselves, we write (mtTemporalGranule C TSET), where TSET is the Cyc
collection of such granules. For example, (mtTemporalGranule NYSE-Mt
NYSETradingDay). We might tell Cyc that the granule size of the
Winter1998OlympicsMt is .01 seconds, but we wouldn't have a collection
of the particular hundredths of seconds involved. So we could make a
mtTemporalGranuleSize assertion about Winter1998OlympicsMt, but not
one about mtTemporalGranule of Winter1998OlympicsMt.
Thus the meaning of SometimesFn and Relevant+SometimesFn is slightly
more complicated than we mentioned above. Namely, they mean that
assertions hold for some moment in that context.
-Another component of each "value along the Time dimension" is a
persistence-distribution. This is a default for how likely it is that
a typical assertion that's made into context C will be true
earlier/later than the time associated with the C. That distribution
d is specified via an assertion of the form (mtTimeDistribution C d),
where d itself will be specified in terms of the appropriate
parameters (see Section 3.1.2.) There will likely be exceptions that
override it, explicitly. That is, an assertion P in context C having
a different persistence distribution: (timeDistribution P d')
For example, if we want to have a 1920sUSA context, it's as if there
were 4 contexts:
TrueThroughout1920sUSA-Mt
TrueSometimeIn1920sUSA-Mt
RelevantThroughout1920sUSA-Mt
RelevantSometimeIn1920sUSA-Mt
From the user's point of view, an interface should let them quickly
and easily find/create a single USA context - USAMt - and then
associate n temporal objects with that context, and then (for each one
of those n temporal objects) enable them to make two yes/no choices
(True/Relevant? and Sometimes/Always?) when assertions are entered,
questions are asked, etc. Those choices could have the form of in/out
pushbuttons whose settings get guessed at, so the user rarely has to
take the time and trouble to change any of those settings. If no
temporal object is explicitly specified, the presumption is that n=1
and that the implicit temporal object associated with the context is
the largest one possible, consistent with all other constraints (such
as the date of invention of the objects mentioned in assertions in the
context).19
In the case of 1920sUSA, we would create a USAMt context, then
associate it with the temporal object that is the decade-long solid
block of time (DecadeFn 1920), which might get reified as, e.g.,
The1920s. We would then make assertions about 1920s America into the
four contexts defined by these four non-atomic terms:
(Relevant+AlwaysFn USAMt The1920s)
(Relevant+SometimesFn USAMt The1920s)
(AlwaysFn USAMt The1920s)
(SometimesFn USAMt The1920s)
Facts and rules that were true throughout the decade would get
asserted into the first of those four contexts, and things true just
sometime during the decade would get asserted into the second
context. Something asserted into the first context would be known to
hold in the second context, because of the guaranteed genlMt
relationship between an ...Always... context and the corresponding
...Sometimes... context. It would be very unusual for anyone to want
to hand-assert anything into the latter 2 contexts; after all, if it's
not relevant to 1920's USA why in the world bother asserting it into a
1920's USA context?
That takes care of the first part of specifying the Time dimension
value for 1920sUSA. The second and final part is to specify a
temporal persistence distribution. E.g., if you are told that P was
true throughout the entire 1920's, how likely is it that P also held
in December of 1919? January of 1933? Etc. To specify that
distribution, we would assert, e.g., (mtTimeDistribution (AlwaysFn
USAMt The1920s) ModernHistoricDecayDistrib).
There would be several assertions about ModernHistoricDecayDistrib,
which would say that it's a normal distribution, its mean is 2 years,
its standard deviation is 3 months, etc. Those assertions about
ModernHistoricDecayDistrib would have to hold in some context at least
as general as (AlwaysFn USAMt The1920s); probably they would hold in a
context broader than just the USA and broader than just the 1920's.
In rare cases we would assert a different distribution for some
individual assertions; e.g., every assertion about who the leader of a
country is, gets a step distribution.
There will almost certainly be different default persistence
distributions for the four specMts of USAMt above, (Relevant+AlwaysFn
USAMt The1920s), (AlwaysFn USAMt The1920s), (Relevant+SometimesFn
USAMt The1920s), and (SometimesFn USAMt The1920s) . E.g., the
probability distribution of the typical ...Sometimes... assertion is
generally much more rapid and spike-like than a typical ...Always...
assertion.
So: to specify the decay pattern of the truth of a typical assertion
in a context C, we cite an instance d of
TemporalPersistenceDistribution; we assert (mtTimeDistribution C d).
For an exceptional assertion P, we override this by asserting
(timeDistribution P d'). TemporalPersistenceDistribution is a subset
of PersistenceDistribution (there are spatial persistence
distributions as well.) Initially, each instance d of
PersistenceDistribution will be spike, step, ramp, uniform, or normal
(bell-curve-shaped), or the appending of two persistence distributions
d1 and d2 - i.e., the value of (appendedDistributionFn d1 d2).
1. #$Spike-PersistenceDistribution - The parameters for this sharp
spike-shaped distribution are specified using the predicates
#$spikeWidth, #$spikePeakValue, #$spikeNonPeakValue, and
#$spikePeakLocation.
2. #$Step-PersistenceDistribution - The parameters for this
step-shaped distribution are specified using the predicates
#$stepLocation, #$stepInitialValue, and #$stepFinalValue. For a
distribution that is a series of steps, we may either introduce a new
type persistence distribution, but a more general solution is to just
have a standard way of forming a compound distribution by appending
simpler ones thus: (#$appendedDistributionFn d1 d2).
3. #$Ramp-PersistenceDistribution - The parameters for this smooth
ramp-shaped distribution are specified using the predicates
#$rampInitialValue and #$rampFinalValue. The ramp's initial
starting/ending location is presumed to be the starting/ending-point
of the temporal object.
4. #$Uniform-PersistenceDistribution - The parameter for this flat
distribution is specified using the predicate #$uniformValue.20
5. #$Normal-PersistenceDistribution - The parameters for this
bell-curve-shaped distribution are specified using the predicates
#$meanDistributionValue and #$standardDeviation. The location of the
mean is assumed to be the midpoint of the piece of time corresponding
to the TemporalObject. In cases where that's not true - i.e., the
distribution is "lopsided", use
#$LopsidedNormal-PersistenceDistribution.
6. #$LopsidedNormal-PersistenceDistribution - The parameters for this
lopsided-bell-curve-shaped distribution are specified using the
predicates #$meanDistributionValue, #$leftStandardDeviation,
#$rightStandardDeviation, and #$meanLocation. In effect this
distribution is like two normal bell-shaped curves (but with different
shapes) that meet at the mean value, wherever that is.
It is not always necessary to create a context just to temporally
qualify an assertion. There are two temporally qualifying modal
operators (the first of which is today's "holdsIn"):
- (holdsAlwaysDuring TTHING P). This is true iff formula P is true at
every moment in the temporal extent of the temporal thing TTHING.
- (holdsSometimesDuring TTHING P). This is true iff formula P is true
at some moment in the temporal extent of the temporal thing TTHING.
3.1.8 When is a formula True?
Suppose P is a Cyc formula, and t is a "moment" (in some contexts C1,
C2,...) If P is a compound "molecular" formula, then:
* (not P) is true at moment t if and only if P is false at moment t
- (and P1 P2) is true at moment t if and only if P1 is true at t and
P2 is true at t etc.
For an "atomic" formula, let's consider the typical case (#$owns term1
term2). That formula holds true at moment t if and only if the
denotations of term1 and term2 stand in the "owns" relationship at
moment t. E.g., suppose Fred owned Spot from 1945-50; i.e., for that
whole time, but not before or after that time period. Then the Cyc
formula (owns Fred Spot) is true at each moment in 1946, and false at
each moment in 1940 and at each moment in 1960. Notice that it
doesn't matter whether either or both of them (Fred and Spot) happen
to be alive in 1940, nor 1960.
In the (AlwaysFn USA TheYear1948), the assertion (owns Fred Spot) is
true, and its negation is false. The same for (SometimesFn USA
TheYear1948).
In the (AlwaysFn USA TheYear1908), the assertion (owns Fred Spot) is
false, and its negation is true. The same for (SometimesFn USA
TheYear1908). Note that it doesn't matter whether either or both of
Fred and Spot were alive in 1908. That does affect the relevance of
those assertions, of course. If either wasn't yet born, then the
assertion is true but most likely not going to be relevant to
reasoning about America in 1908.
Neither (owns Fred Spot) nor its negation would hold true in the
context (AlwaysFn USA The1940s). Both (owns Fred Spot) and its
negation would hold true in the (SometimesFn USA The1940s). That
means that Cyc had better not use most rules of inference, such as
modus ponens, within that context. There is a class of contexts
NonInferrableMt to which this belongs, having the property that in
general just because one can deduce Q from assertions in that context
does not means that one can then safely just add Q there. Another
example of such a context would be the one representing sentences that
Fred has uttered. Just because he's said "A and B" doesn't mean that
he's ever said "B and A." In the case of a ...Sometimes... context
SC, we can do some reasoning safely, such as combining one of its
assertions with one that's known to hold across the entire time
interval of SC.
The denotations of the expressions term1 and term2 might change over
time. For example, the assertion (livesIn (PresidentFn USA)
(CapitalCityFn USA)) is true at all (and only) those moments when the
then-current President of the United States lives in the city that is
then the capital of the USA. E.g., it is true for George Washington
living in Philadelphia for a few years, and for Jerry Ford living in
Washington, D.C. for a few years, and so on.
Subabstractions haven't gone away, but the preceding semantics should
enable us to deal directly with whole individuals even when making
temporally qualified assertions.
Just because (p x y) is true at moment t doesn't mean necessarily that
x temporally subsumes t. For example, (inventor ThomasEdison
Phonograph) is true today.
3.2 Dimension: TypeOfTime
The default type of time period in which the action takes place, the
actors are situated, etc, for the assertions in this theory. For
example, a context of ModernWesternSleeping might have Night or
NapTime as its TypeOfTime. Other possible values along this dimension
will be NATs (non-atomic terms) constructed by applying some sort of
"during" operator to some event or process; for example: during an
intermission, during an election campaign, and so forth. Cyc's
current vocabulary for talking about events may already suffice for
the purpose of stating these values. If not, the
...Sometimes... functions and operator, below, should fill any gap.
Note that this dimension is relatively independent of Time. Since the
TypeOfTime is going to be (one or more) Collections, the genls
predicate induces a partial order on the TypeOfTime dimension values.
Putting this all together, a setting for this dimension will be a set
of one or more TypeOfTime instances. Appropriate superTimeInterval
assertions will be made in the KB.
We use four functions here similar to what we did for Time, in the
previous section. Namely:
(#$Relevant+AlwaysTypeFn C TypeOfTime) = C1 means that the assertions
in context C1 are precisely those assertions that hold in C and which
happen to be both true and relevant throughout the entire temporal
extent of each temporal object t which is an instance of TypeOfTime
(which must itself be a TemporalThingType and is usually a
TemporalObjectType). C1 is akin to a "during an entire..."
restriction; e.g., could be used to express the idea that P is true
during every moment of every intermission, during every instant of
every Friday, etc. (Naturally, these can be stated as defaults, with
exceptions.)
Here are some sample legal values for what TypeOfTime could be - i.e.,
these are TemporalThings and (except for Breathing) also
TemporalObjectTypes: Swallowing, 1998WinterOlympicEvent,
USCabinetMeeting, ChristmasHoliday, and Breathing.
Here are some examples of subsets of TemporalObjectType; instances of
these could be legal values for TypeOfTime: #$SportsCategoryType,
#$AnnualEventType, #$WeeklyEventType, #$ClimateCycleType,
#$ExclusiveTreatment, #$CourseOfStudyType,
#$DrugAdministrationRouteType, #$CalendarCoveringType,
#$DayOfMonthType, #$TimeOfDayType, #$TemporallyDisjointIntervalType,
#$ConveningEventType, $DayOfYearType, #$MonthOfYearType, and
#$CalendarSeasonType.
(#$Relevant+SometimesTypeFn C TypeOfTime) = C2 means that the
assertions in context C2 are precisely those assertions that hold in C
and which happen to be both true and relevant during at least some
portion of the temporal extent of each t which is an instance of
TypeOfTime (which must itself be a TemporalThingType (a spec of
TemporalThing) and usually also turns out to be an instance of
TemporalObjectType). Note that (genlMt (#$Relevant+SometimesTypeFn C
x) (#$Relevant+AlwaysTypeFn C x)) - that holds true for all C and x.
Note that C2 will be akin to a "at some time during a..." restriction;
e.g., could be used to express the idea that P is true at some time
during an intermission, at some time during a meal, at some time on a
Friday, etc.
(#$AlwaysTypeFn C TypeOfTime) = C3 means that the assertions in
context C3 are precisely those assertions that hold in C and which
hold true throughout the entire temporal extent of every t which is an
instance of TypeOfTime (which must itself be an instance of
TemporalThingType and usually also TemporalObjectType). Note that -
for all C and x - the following will necessarily be true: (#$genlMt
(#$AlwaysTypeFn C x) (#$Relevant+AlwaysTypeFn C x)).
(#$SometimesTypeFn C TypeOfTime) = C4 means that the assertions in
context C4 are precisely those assertions that hold in C and which are
true during at least some portion of the temporal extent of each
temporal object t which is an instance of TypeOfTime (which must
itself be an instance of TemporalThingType and usually a
TemporalObjectType). Note: C4 will be a specMt of C1, C2, C3, above.
For some value of TypeOfTime, C4 = C.
It is not always necessary to create a context just to temporally
qualify an assertion to hold during a certain type of time. There are
two new temporally-qualifying modal operators (besides
holdsAlwaysDuring and holdsSometimesDuring) for this purpose:
- (holdsAlwaysDuringA TOBJTYPE P). This is true iff formula P is true
at every moment in the temporal extent of each TemporalThing which is
an instance of TOBJTYPE (which itself must be a TemporalThingType and
is probably a TemporalObjectType.
- (holdsSometimesDuringA TOBJTYPE P). This is true iff formula P is
true at some moment in the temporal extent of each TemporalThing which
is an instance of TOBJTYPE (which itself must be a TemporalThingType
and is probably a TemporalObjectType.
3.3
Dimension: GeoLocation
The default geographic location of the actors, events, etc. mentioned
in the assertions in this theory. In many ways this is analogous to
the Time dimension (see Section 3.1).
- Elements of this dimension are partially ordered by containment.
- Each assertion can have a Some/All/... tag that indicates whether
it's true somewhere in, or everywhere in, that geographic region.
That can often be inferred by examining the main predicate (and other
terms) appearing in the assertion, or may even be weakly inferred by
the context as a whole. Thus a legal context might by default predict
that its assertions will have an "All" GeoLocation bit; but the
predicate livesIn might predict that its assertions are by default
"Some" (for example, Ronald Reagan lives in California - meaning that
he lives somewhere in California but he doesn't live everywhere in
California.)
- Each assertion has a spatial range over which its truth value
changes from True to False. That might be a crisp step function, but
often is more like a distribution. of probabilities. For instance, in
a context having New York State as its GeoLocation, we might assert
"It's snowy in the winter." This remains true outside New York, but
by the time one gets to Ecuador it's false. Rather than handcraft a
million special-purpose distributions, and have some complicated
reasoning mechanism, we expect that it will suffice to have a handful
of commonly occurring distributions, and to specify one of those and
give zero or more parameters, just as we do for the Time dimension.
In fact, they are the same distributions as used there - instances of
PersistenceDistribution.
- Location is typically given relative to something else, such as:
the North Pole and other features on the surface of the earth;
position in our solar system relative to the sun and the planets;
on the dark side of the moon;
on the surface of the sun;
in the Gulf Stream;
etc.
- Again as with Time, there is a difference between where
geographically something is True versus where it is Relevant. The
temperature at which igloos melt is more relevant in Alaska than
Ecuador, though it's equally true in both places.
Of course there are some differences between Time and GeoLocation, if
nothing else because space is more than just one-dimensional. Richer
notions of connectedness, convexity, compactness, paths,
junctions/branchings, etc. are possible than in the one-dimensional
Time case.
Putting that all together, then, here is how we represent GeoLocation
in Cyc:
- One portion of a context's content is just "true" for some spatial
region (usually some geographic region) the rest is both true and
"relevant." One portion of a context's content holds throughout a
whole spatial region gi, the rest just holds at some places in that
region. These two binary choices effectively carve each context up
into four discernable pieces.21 In Cyc there are 4 functions that
connect a context to these 4 more specialized (and probably
non-reified) contexts. See Figure 3b.
(#$Relevant+EverywhereFn C t) = C1 means that the assertions in
context C1 are precisely those assertions that hold in C and which
happen to be both true and relevant throughout the entire spatial
extent of the SpatialThing t.
(#$Relevant+SomewhereFn C t) = C2 means that the assertions in context
C2 are precisely those assertions that hold in C and which happen to
be both true and relevant in at least some portion of the spatial
extent of t (a #$SpatialThing.) Note that (for all C and t) (genlMt
(#$Relevant+SomewhereFn C t) (#$Relevant+EverywhereFn C t)).
(#$EverywhereFn C t) = C3 means that the assertions in context C3 are
precisely those assertions that hold in C and which hold true
throughout the entire spatial extent of t. Note that (for all C and
t) (#$genlMt (#$EverywhereFn C t) (#$Relevant+EverywhereFn C t))
(#$SomewhereFn C t) = C4 means that the assertions in context C4 are
precisely those assertions that hold in C and which are true in at
least some portion of the spatial extent of t. Note that C4 will be a
specMt of C1, C2, C3, above. For some t, C4 = C.
- Another component of each "value along the GeoLocation dimension" is
the granule size and, if known, a more absolute
geographic-location-based characterization of the granules. This
indicates how small a piece of space is before it's considered an
indivisible point. We write (mtSpatialGranuleSize C t) to indicate
that context C has, as such a granule size, the size of the duration
of spatial object t.
If we know not just the right size, but the particular spatial
granules themselves, we write (mtSpatialGranule C GSET), where GSET is
the Cyc collection of such granules. For example, (mtSpatialGranule
GlobalWeatherForecastingMt HadleyCell), where the world is divided up
into Hadley cells but no finer. We might tell Cyc that the spatial
granule size of the KentuckyDerbyHorseraceMt is the size of a horse's
nose, but we wouldn't carve up space into coordinate axes labeled in
terms of horse's noses. So we could make a mtSpatialGranuleSize
assertion about KentuckyDerbyHorseraceMt, but not one about
mtSpatialGranule of KentuckyDerbyHorseraceMt.
Thus the meaning of SomewhereFn and Relevant+SomewhereFn is slightly
more complicated than we mentioned above. Namely, they mean that
assertions hold for some point in that context C (i.e., for 1+ spatial
points in each of C's associated spatial objects.)
- Another component of each "value along the GeoLocation dimension" is
a persistence-distribution. This is a default for how likely it is
that a typical assertion that's made into context C will be true
somewhere outside the GeoLocation of C. That distribution d is
specified via an assertion of the form (mtSpaceDistribution C d),
where d itself will be specified in terms of the appropriate
parameters (see Section 3.1.2.) There will likely be exceptions that
override it, explicitly. That is, an assertion P in context C having
a different persistence distribution: (spaceDistribution P d')
NOTE: In this and the following sections, we use "SpatialThing"
repeatedly but, in the current vocabulary, this would actually be
#$SpatialThing-Localized. Furthermore, we use the term
SpatialThingType which does not exist in the current Cyc vocabulary,
and - if it is not created and added there - should be taken to be
just Thing; where we say "...a SpatialThingType", or "an instance of
SpatialThingType", please take that as "a spec of SpatialThing".
Furthermore, we use the term SpatialObjectType which, in the current
Cyc vocabulary, does not exist and should be taken to be just
ObjectType. Either the missing terms should be added to the Cyc
ontology, or else the above substitutions (discussed in this
paragraph) should be made, in this document, before it publication.
For example, if we want to have a 1920sUSA context, it's as if there
were 4 contexts:
TrueEverywhereIn1920sUSA-Mt
TrueSomewhereIn1920sUSA-Mt
RelevantEverywhereIn1920sUSA-Mt
RelevantSomewhereIn1920sUSA-Mt
From the user's point of view, an interface should let them quickly
and easily find/create a single context - e.g., Farming - and then
associate n spatial objects with that context - e.g., the continental
USA - and then (for each one of those n spatial objects) enable them
to make two yes/no choices (True/Relevant? and Somewhere/Everywhere?)
when assertions are entered, questions are asked, etc. Those choices
could have the form of in/out pushbuttons whose settings get guessed
at, so the user rarely has to take the time and trouble to change any
of those settings. If no spatial object is explicitly specified, the
presumption is that n=1 and that the implicit spatial object
associated with the context is the largest one possible, consistent
with all other constraints (such as the date of invention of the
objects mentioned in assertions in the context). Note that
TemporalThings associated with the context would also exist, and each
have a pair of pushbutton settings to specify true/relevant and
sometimes/always for the Time dimension of that context.
In the case of the context C99 for "Automobiles in the 1920s USA", we
would create an AutomobilesMt context, then associate it with the
temporal object that is the decade-long solid block of space (DecadeFn
1920), and associate it with the spatial object that is the
continental United States of America - say that's been reified as
USA-Continental.. We would then make assertions about automobiles in
1920's America, asserting them into the appropriate one (or more)
contexts defined by these four non-atomic terms:
(Relevant+EverywhereFn AutomobilesMt USA-Continental)
(Relevant+SomewhereFn AutomobilesMt USA-Continental)
(EverywhereFn AutomobilesMt USA-Continental)
(SomewhereFn AutomobilesMt USA-Continental)
Facts and rules that were true throughout the country (that decade)
would get asserted into the first of those four contexts, and things
true just in certain parts of the USA during the decade would get
asserted into the second context. Something asserted into the first
context would be known to hold in the second context, because of the
guaranteed genlMt relationship between an ...Everywhere... context and
the corresponding ...Somewhere... context. It would be very unusual
for anyone to want to hand-assert anything into the latter two
contexts; after all, if it's not relevant to "Automobiles in the
1920's USA" why would anyone deem it worth asserting it into that
context?
Point 6 describes how this dimensionalizing of contexts is already
beginning to apply, even though we've just started enumerating the
dimensions:
Point 6: Starting with a context about "daytime driving automobiles in
rural 1920's America..." we can use the Time dimension to factor out
the "1920's" part of what the context was, the TypeOfTime dimension to
factor out the "daytime" part, the GeoLocation dimension to factor out
the "America" part, and we will use the TypeOfPlace and Topic
dimensions, respectively, to filter out the "rural" and "driving
automobiles" parts. In this case, the whole context will be uniquely
specified by specifying a set of values on a handful of our
dimensions. There may not be any extra assumptions at all that have
to get stated; the context C may just receive some assertions. In
other words, C is just a set of assertions plus a set of values along
a few of our dimensions.
That takes care of the first part of specifying the GeoLocation
dimension value for this context. The second and final part is to
specify a spatial persistence distribution. E.g., if you are told
that P was true throughout the entire continental USA, how likely is
it that P also held in Toronto? In Cairo? Etc. To specify that
distribution, we would assert, e.g.,
(mtSpaceDistribution
(EverywhereFn AutomobilesMt USA-Continental)
ModernCultureSpatialDecayDistrib)
There would be several assertions about
ModernCultureSpatialDecayDistrib, which might say that it's a normal
distribution, its mean is 10 miles, its standard deviation is 1 mile,
etc. Those assertions about ModernCultureSpatialDecayDistrib would
have to hold in some context at least as general as (EverywhereFn
AutomobilesMt USA-Continental); probably they would hold in a context
broader than just the USA, broader than just cars, etc.
In rare cases we would assert a different distribution for some
individual assertions; e.g., every assertion about who the leader of a
country is, gets a step distribution. That was true in Time (x is the
leader starting and ending at crisp time-points, usually) and it's
also true in GeoLocation (x is the leader of a region with precise
borders, usually within those borders, s/he is the leader, and outside
those borders s/he is not the leader. Period.)
There will almost certainly be different default persistence
distributions for the four specMts of AutomobilesMt above.
So: to specify the spatial decay pattern of the truth of a typical
assertion in a context C, we cite an instance d of
SpatialPersistenceDistribution; we assert (mtSpaceDistribution C d).
For an exceptional predicate p, we override this by asserting
(predSpaceDistribution p d'). For an exceptional assertion P, we
override this by asserting (spaceDistribution P d'').
SpatialPersistenceDistribution is a subset of PersistenceDistribution
(as we discussed above, there are temporal persistence distributions
as well.) Initially, each instance d of PersistenceDistribution will
be spike, step, ramp, uniform, or normal (bell-curve-shaped),
lopsided-normal, or the appending of two persistence distributions d1
and d2 - i.e., the value of (appendedDistributionFn d1 d2). For the
parameters corresponding to how one specifies each type of
distribution, please see the listing above, near the end of
Sec. 3.1.7.
It is not necessary to create a new context just to spatially qualify
an assertion. There are two spatially qualifying modal operators that
can do that directly:
- (holdsEverywhereIn STHING P). This is true iff formula P is true at
every point in the spatial extent of the spatial thing STHING.
- (holdsSomewhereIn STHING P). This is true iff formula P is true at
some point in the spatial extent of spatial thing STHING.
3.4 Dimension: TypeOfPlace
The default type of place in which the action takes place, the actors
are located, etc, for the assertions in this theory. For example, a
context of ModernWesternSleeping might have Bedroom and HotelRoom as
its TypeOfPlace. A Cooking context might have Kitchen (private or
commercial) as its TypeOfPlace.
Note that this dimension is relatively independent of GeoLocation.
More precisely, it depends somewhat on Culture, and Culture in turn
correlates with GeoLocation. For instance, most activities in Japan
are part of JapaneseCulture, which in turn has the sleeping take place
by default in the living room, not in a separate bedroom.
Not all the values here are culture-related. E.g., Underwater,
Underground, Arboreal, Airborne, Outdoors, a small claustrophobic
place, a large agoraphobic place, a place with no (significant)
atmosphere, a dark place, etc.
Since the TypeOfPlace is going to be (one or more) Collections, the
genls predicate induces a partial order on the TypeOfPlace dimension
values. Typically, combinations of repeated genls (e.g., Kitchen to
Room) and superLocations (e.g., Kitchen to House) will be allowed.
Another useful partial order on Type Of Place instances A and B will
be provided by axioms of the form (=> (isa X A) (thereExists Y (and
(isa Y B) (physicalDecompositions X Y))))
and
(=> (isa X A) (thereExists Y (and (isa Y B) (physicalDecompositions Y
X)))).
Putting this all together, how do we represent TypeOfPlace in Cyc? We
use four functions here similar to what we did for the previous
dimensions. Namely:
(#$Relevant+EverywhereTypeFn C SPLACETYPE) = C1 means that the
assertions in context C1 are precisely those assertions that hold in C
and which happen to be both true and relevant throughout the entire
spatial extent of every spatial object x which is an instance of
SPLACETYPE (which must itself be a SpatialThingType and is usually a
TemporalObjectType). C1 is akin to a "throughout an entire..."
restriction; e.g., could be used to express the idea that P is true
throughout all parts of every city (such as the presence of buildings
might be), in every part of every restaurant (such as a no-smoking
policy might be, in the context whose GeoLocation was California and
whose Time was the 1990's), etc.
Here are some sample legal values for what SPLACETYPE could be - i.e.,
these are SpatialThingTypes and (except for the last) also
SpatialObjectTypes: Room, Lawn, Jet Fighter Cockpit, Wooded Area.
(#$Relevant+SomewhereTypeFn C SPLACETYPE) = C2 means that the
assertions in context C2 are precisely those assertions that hold in
C and which happen to be both true and relevant at least somewhere in
the spatial extent of every x which is an instance of SPLACETYPE
(which must itself be an instance of SpatialThingType, and is
probably also an instance of SpatialObjectType.) Note: (genlMt
(#$Relevant+SomewhereTypeFn C x) (#$Relevant+EverywheresTypeFn C x))
for all C and x. Note that C2 will be akin to a "somewhere in a..."
restriction; e.g., could be used to express the idea that P is true
at some place in each hotel lobby (such as the presence of a checkin
desk), somewhere in each restaurant (such as a kitchen door),
somewhere in each city (such as a city hall), etc.
(#$EverywhereTypeFn C SPLACETYPE) = C3 means that the assertions in
context C3 are precisely those assertions that hold in C and which
hold true throughout the entire spatial extent of every x which is an
instance of SPLACETYPE (which must itself be an instance of
SpatialThingType and usually also be an instance of
SpatialObjectType). Note that (for all C and x) the following will
necessarily be true:
(#$genlMt (#$EverywhereTypeFn C x) (#$Relevant+EverywhereTypeFn C x)).
(#$SomewhereTypeFn C SPLACETYPE) = C4 means that the assertions in
context C4 are precisely those assertions that hold in C and which are
true in at least some portion of the spatial extent of every spatial
thing x which is an instance of SPLACETYPE (which must itself be an
instance of SpatialThingType and usually also SpatialObjectType).
Note that C4 will be a specMt of C1, C2, C3, above. For some value of
SPLACETYPE, C4 = C.
It is not always necessary to create a context just to temporally
qualify an assertion to hold during a certain type of space. There
are two new spatially-qualifying modal operators (besides
holdsAlwaysDuring and holdsSometimesDuring) for this purpose:
- (holdsEverywhereInA SOBJTYPE P). This is true iff for each spatial
object SOBJ which is an instance of SOBJTYPE (which in turn must be an
instance of SpatialThingType and usually also is an instance of
SpatialObjectType), the formula P is true at every spatial point x in
the spatial extent of SOBJ.
- (holdsSomewhereInA SOBJTYPE P). This is true iff for each spatial
object SOBJ which is an instance of SOBJTYPE (which in turn must be an
instance of SpatialThingType and usually also is an instance of
SpatialObjectType), the formula P is true at some spatial point x in
the spatial extent of SOBJ.
Before we go on to the next dimension, let's pause and consider the
issue of "prohibited regions" of n-space. Sometimes the assertions
we've made about some context-dimension-setting predicates constrain
or even fully determine the possible values for other such predicates.
Here are a couple ways this can happen:
- for all P, (holdsEverywhereInA Building P) => (holdsEverywhereInA
House P) which says: if P holds throughout every building, it must
hold throughout every house. The fancy way to say that is: the
dimension-value-setting predicate (in this case, holdsEverywhereInA)
transfers through the partial ordering relation (in this case, genls -
the supersets relation) that holds between the arg1types of the first
predicate. A related example of (transfersThrough holdsEverywhereInA
implies): for all P and Q,
if P=>Q and(holdsEverywhereInA Building P), then (holdsEverywhereInA
Building Q)
- If someone has taken the trouble to assert [for some P], in context
C, (holdsEverywhereInA Building P), then it's a pretty good bet that
C's Time value intersects the time period starting when people began
having and using buildings.
3.5 Dimension: Culture (restrictions on the AgentType)
This dimension is meant to specify the default culture to which
intelligent actors (typically people) belong - i.e., the actors who
are mentioned in assertions in this theory. Cultures are ordered by
subCulture. Several types of assertions transfer through subCulture,
including most aspects of codes of conduct. The points of this
dimension therefore organize into a lattice. It is not at all
tree-like, though, due to the large number of somewhat-independent
subculture "types" or "sub-dimensions" 23:
political culture (Democrat, Facist, Libertarian, ...)
sexual culture (male, female)
sexual orientation culture (heterosexual, ...)
age culture (young,..., adult ,..., old)
generation culture (Renaissance, of the 1960's, generation X...)
religious culture (Atheist, Fundamentalist Jew, Moslim, Catholic, ...)
ancestral culture (of Irish descent, etc.)
geo-political culture (American, European,...)
regional culture (midwestern, east-coast, west coast, ...)
region-type culture (urban, rural, ...)
economic/work culture (idle rich, working academicians, Protestant
ethicees,...)
legal culture (based on aspects of the codes of conduct/enforcement)
Note that Culture need not be a geopolitical thing. There's a Hacker
culture, a Cult culture, a FishingCulture, a QuiltingCulture, a
GenerationX culture, etc.
In Cyc we specify the Culture constraint via a predicate called
mtAgentType. I.e., by asserting: (mtAgentType C HCT) where C is a
context, and HCT is a HumanCultureType. Multiple mtAgentType
assertions are interpreted as conjoining; i.e., the default agent in
that context belongs to all those agent-types. Some of these
conjoinings are worth naming, such as PoorWhiteSouthernBaptistCulture,
or HardWorkingKoreanImmigrantsToUSA.
A single theory (i.e., context) may very well have two or three
specific Cultures whose disjunction (i.e., union) is meant to be the
Culture of the context. For instance, consider an
AmerianSoldiersInVietnam context, in which American and Vietnamese
cultures are both relevant (the assertions assume some mixture of the
two cultures, but not their intersection.) We have a special
predicate to define that union of cultures, namely (cultureUnion X Y).
This is associative, so 3+ cultures can be "unioned" by just having
nested cultureUnion assertions. Most of these unions aren't worth
reifying. This raises the following point:
Point 7: Most "settings" for a context - for any one full value of any
one single dimension of context-space - are not worth naming or
remembering.
More complicated specifications may have to use the more general
domainAssumptions predicate; see the Let's dimension, below. E.g., to
express USSoldiers&LaotianCivilians we could use (cultureUnion
USSoldiers LaotianCivilians) if they both are reified, otherwise we
could use domainAssumptions to say that (in that context) if x was
American they were a soldier, and if Laotian then a civilian, and in
the culture dimension just assert the full cultureUnion.
3.6 Dimension: Sophistication / Security
This dimension captures the notion that only certain people
can/may//should/do/will know the material that is the content (and
assumptions) of a context. A detailed medical context might contain
information known only by physicians who specialize in that area. A
company's salary data might be known only by Human Resources staff of
that company. A listing of the latest stock tips might be known only
to those who have paid for them. So the limitations to someone
knowing those assertions may be educational, legal, etc. There may be
enough distinctions between Sophistication and Security that these
should eventually be split into two completely separate dimensions22
but in Cyc they are both specified, as we discuss below, using the
same quinary predicate mtAccessConstraint.
3.6.1 Sophistication
"Sophistication" refers to how sophisticated someone would have to be,
in order
- to readily learn them(in this form) if they are taught, without lots
of prerequisites
- to understand them and recognize them as true, once they clearly
stated
- to already be familiar with the assertions, at least theoretically
(this can mean, e.g., being able to infer the assertions quickly and
automatically, from a few hints)
- to have already deeply assimilated (implications of) the content of
the assertions
This is"can", not "may." It generally means
understanding/recognizing/ knowing/... the predicates, the
collections, etc. mentioned in assertions in the theory. It also may
depend on how verbose and complicated the assertions are, the sheer
number of terms, etc.
We could define a plethora of more specialized attributes (of a
user/peruser) that are related to and in a way come together to define
that person's sophistication: educational level, age, job,
places-visited, etc. In many ways, this set of attributes subsumes
all of the previously-mentioned Culture dimension predicates, with two
exceptions: (1) in this case we aren't describing the agents "talked
about" in the content of the context, but rather the agents who
already know, or could learn, or couldn't learn, that content; and (2)
some of the Culture sub-dimensions23 are at best only weakly relevant
to comprehension: gender, religion, etc.
One bit of good news is that each of these in turn - education level,
places-visited, age, etc. - is describable via a simple linear scale
or a well-defined set of possible settings. The other good news, as
with most other dimensions, is that most of the time the person doing
the asserting (or asking) is not going to manually tinker with these
settings, but rather have them copied from similar/related assertions
(or questions) and/or have them inferred by the system automatically
(from the prior context, the current task, a model of the person who
is stating/asking, and of course from the form and terms of the
assertion/question itself.)
3.6.2 Security
"Security" refers to what sorts of authorization someone would have to
have, in order to be permitted to see, use, modify, etc. the
assertions in this theory. This might depend on their being employed
by a certain company, being over some legal minimum age, having
qualified/registered in some fashion with some organization, etc. The
types of rights are probably similar to those generally granted by
database systems and operating systems.
Conversely, someone might wish to only browse through assertions which
they have the right to edit. One interesting level of access might be
"used in non-top-level inference", which means you can't see the
assertion, or trivially see it being used, but it can be deeply used
in solving some sub-sub-...-goal of the problem.
At any rate, the Security authorizations are likely to be specified in
a "rights" matrix, whose rows are the contexts and whose columns form
the Security sub-dimensions23: who can see this, who can use this, who
can edit this, who can delete this, and so on.
In Cyc, here is how this is all expressed:
- There is a term called #$TheUser which denotes the `current user'
who is talking to Cyc - i.e., logged in and running the current Cyc
image. Note that at any moment there may actually be many current
users of a single Cyc image, communicating with it through various
sorts of API interfaces (HTML-based browser, telnet Application
Program Interface (API) connection, etc.) Each communication in
effect defines a local ephemeral value for #$TheUser. The point: here
is a place for Cyc to keep track of each user's relevant
characteristics (including authorization and sophistication level.)
Much of this will be inferred from groups to which the user belongs,
jobs s/he holds, their date of birth, their country of citizenship,
and so on.
- (#$mtAccessConstraint C P necessary/sufficient? type?
content/assumptions?) expresses the constraint P. C is a context, P
is a Cyc formula, necessary/sufficient? is either #$Necessary or
#$Sufficient, content/assumptions? is either #$Content or
#$Assumptions, and type? is an #$MtAccessClass which means it is one
of these 6 values: #$CapableOfKnowing, #$TheoreticalKnowing,
#$InternalizedKnowing, #$AccessRights, #$AdditionRights,
#$DeletionRights. If necessary/sufficient? is #$Necessary, this means
that #$TheUser must satisfy the constraint P, in order for the system
to conclude that they can/should/do have access of type type? to the
content or assumptions of context C. In other words, if the user
fails that test P, then they must not have that mode of access to that
material. If necessary/sufficient? is #$Sufficient, this means that
if #$TheUser satisfies the constraint P then Cyc can infer that they
can/should/do have access of type type? to that material: they could
learn it, they probably already know it abstractly, they act as though
they know it, they are allowed to inspect/browse it, they are allowed
to assert or unassert it. Some of these imply others; some are
inconsistent with others; but mostly they are independent combinations
which each make sense.
Note that the formula P probably mentions #$TheUser. For example, P
might be a formula like: (#$levelOfEducation #$TheUser
#$HighSchoolEducation) or - omitting #$'s - (speaks TheUser French) or
(employedBy The User GlaxoWellcomeInc). It's hard to argue that we
should reify those sorts of P-values, but efficient inference will
probably dictate doing so sooner or later, for the more common
categories of access constraints.
We regret having to use a quinary (5-argument) predicate like this -
mtAccessConstraint - but otherwise there would be 24 more specialized
binary predicates (taking just C and P as their arguments) for the
knowledge enterer to learn. We may decide to go ahead and also define
24 specialized predicates, or not - or at least the few which capture
the most-often-used values of the final 3 arguments. E.g.,
#$necessaryMtContentAccessRightsConstraint.
Note that if there are multiple mtAccessConstraints with the same
arguments for everything except P, then the meaning (which depends on
the 3rd argument) is as follows: for multiple necessary tests P1,
P2,... (i.e., the 3rd argument is #$Necessary), they must all be
satisfied; for multiple sufficient tests P1, P2,... any one of those
tests suffices.
3.7
Dimension: Topic
Given a context C, what is it "about"? It could be about a person, a
group of people, a field of study, a type of event, a particular
event, an occupation, an academic discipline, a novel or mythos,
preparing for a certain event or kind of event, etc.
Each assertion in the context is, by default, relevant to and helping
to talk about and explain and interrelate the things that C is about.
The basic hypothesis about Topics - and for that matter about each
dimension of context-space - goes something like this: If you limit
your attention to one such topic, then fruitful inference will occur
within that clump of assertions. I.e., most of the reasoning we will
want and need to do, to solve some particular problem, is likely to be
restricted to one or a small number of particular topics.
Conceptually, there might be several sub-dimensions23 of this
dimension, since there is no one correct way of organizing subject
matter.
- We can have separate sub-dimensions23 for each standard subject
classification hierarchy (Dewey decimal system, LC, Colon, Bliss, UDC,
Yahoo, UMLS, the Art & Architecture Thesaurus, Cyc itself, HPKB chart
G1, newspaper classified ads, newspaper sections, encyclopedia topics,
the Outline of Cultural Materials, etc.)
- Yet another (species of) sub-dimension23 of Topic is one organized
around a hierarchy of typical goals that actors have, typical subgoals
that help achieve or advance those goals, and so on.
- Yet another sub-dimension23 of Topic could be based on academic
field boundaries, such as typically are found in universities today.
Consider a context whose topic is "shipwrecks and people and fish".
Each assertion in the context will probably refer to one or more of
those three terms, or to elements of one or more of those three
collections; moreover, the assertions will likely interrelate (an
element of) one of those three terms to (an element of) another of
those three terms.
Note that having (some aspect of) time/location/etc. as a Topic is
quite different from having a setting for the Time, Location,
etc. dimensions. The topic of "time" is one which will have
assertions made about it in many different cultures, different eras,
different levels of granularity, etc. but it is far far less pervasive
than the Time dimension, for which there will generally be some
setting for every context.
This may very well turn out to be the most useful dimension for
separating out large existing "clumps" of assertions in the Cyc KB,
like the content of the current huge HumanActivitiesMt. One could
write arbitrary CycL expressions to precisely denote particular topics
(the education of 5-year-olds, international arms negotiations,
extended family social events that have a joyous tone to them, etc.)
But reasoning about the relative relevance between two topics if
described via arbitrary CycL like that could be arbitrarily
complicated. To cut through that complexity, we will just let each
Topic "setting" be a set of Cyc terms, no more and no less. This means
that new Cyc terms will be added to demarcate topics which are worth
distinguishing but which (currently) don't exist in Cyc. The
interpretation is that all the assertions in a context are "about"
(one or more terms in) its topic; in Cyc, this means that each
assertion which is in the content of the context should explicitly
mention one or more of the collections (or instances of such),
predicates, etc. which are that context's Topic setting.
The relation "subtopic" is much more complicated than "subset." There
are many cases where a topic's subtopics are not subsets of it; e.g.,
"FreshwaterAlgae" and "Dam-building" are sub-topics of "Rivers",
though they aren't subsets, elements, etc. of #$River. And there are
many cases where a set's subsets are not subtopics of it; e.g.,
"Thing" ( "RealNumber" ( "NaturalNumber" ( "EmptySet" but they are
part of the disparate topics of ontology, real analysis, number
theory, and set theory.
There are a relatively small number of questions which characterize
what we colloquially mean by a topic being "about" x. E.g., if x is a
tangible thing, when was it discovered/invented, by whom, etc.; what's
it made of, its shape, its internal structure; how and where and when
is it produced/destroyed/sold/kept, and why; what is it used
for/in/by/...; and so on. If x is an action, when and where does it
take place, and why; what pre- and post-requisite conditions are there
on its performance; who are the performers and other actors and their
roles; what about the first/next/last time it did/will occur; and so
on. Regardless of what x is, What are some extreme cases of this, or
other special cases of it? All of those questions also can lead from
a topic to one of its subtopics, which is why that relation is so much
more complicated than subset.
So there is a new predicate subTopic, which interrelates 2 Cyc
contexts, and a new predicate propositionalInfoAbout which
interrelates a context and a term (to express the notion that that
context is "about" that term.)
Here is a more complete listing of questions that define the notion of
sub-topic, and hence should strongly influence the subTopic and
propositionalInfoAbout values.
- If the topic is some relatively short-term practical task at hand,
such as opening a door:
inputs needed (including energy, information, and physical materials)
tools and equipment required/involved
physical situation, configuration, and location
currently governing codes and standards
methods, plans, scenarios
particular problem set/situation faced
desired outcomes, products, effects, outputs, and by-products
persons/interests to be served
persons or other agents who might assist or thwart success
access and transport to the task activity area
financial/commercial consequences of task
any likely or feasible thing that would alter the outcome
- If the topic is some relatively long-term task at hand, then include
these as well:
development of methodology over time
commercial practice in the field
spectrum of participants and players
changes in governing codes and standards
political (economic, military, etc.) consequences
building the skills needed; training, education
- If the topic is a task or even a tangible thing in the world, then
include these:
the origins of the task/thing
how it was dealt with historically
the fundamental underlying principles (and prerequisite knowledge)
classifications of sub-varieties of task type or thing type
literary or cultural role of the task type or thing type
social role and effects of task type or thing type
fine physical or information structure of the things involved
implications for philosophy, science, history
representation of task or thing in formal systems
are the ultimate goals of the task/thing really worth pursuing?
analogous situations in other fields; parallels
So how exactly is this represented in Cyc? We use these two binary
predicates:
(#$propositionalInfoAbout C TERM) which means that the context C is
`about' the reifiable term TERM, i.e. it is a #$Microtheory with
assertions concerning TERM. For example, a context which is the
propositional content of a portrait of George Washington might have
#$GeorgeWashington as the only TERM of this satisfying this predicate
(i.e., the only value of TERM for which (#$propositionalInfoAbout C
TERM) holds.)
(#$subTopic C1 C2) which means that context C2 is a subtopic of
context C1. Note that propositionalInfoAbout often24 transfers
through subTopic.
3.8 Dimension: Granularity
There are again several sub-dimensions23 here; the two-page chart near
the end of Miller's Living Systems book gives a good summary of some
of these, as he goes from molecular to cellular to organ to organism
to society level. There is a hierarchy of integrative levels, in
which things at one level combine to form things at the next higher
level, such as cells coming together to form an organ, organs coming
together to form an organism, etc. The reason for keeping these
levels separate, though - for having this dimension at all - is that
assertions at one level do not simply translate up or down to the next
level. Each level is almost its own world; atomic collisions don't
directly come up often in solving problems in British Immigration Law,
and vice versa. Moving from level to level even the name of the
academic field changes - e.g., from Sociology to Psychology to
Physiology to Molecular Biology to Chemistry to Physics. Here are
some of the types or sub-dimensions involved:
- What sized objects, events, object-parts, time-periods, subevents,
organizations, etc. are relevant to this context? In particular, more
fine-grained ones are not mentioned nor needed for reasoning within
this context. Also, it's usually the case that much coarser-grained
ones are also not mentioned or needed within this context. For
instance, when reasoning about a baseball's trajectory, neither
particular individual atoms nor particular galaxies (even the Milky
Way) are likley to be taken into account.
- What specificity of classes (collections), relationships,
measurements, etc. are relevant to this context? In particular, more
fine-grained ones are not mentioned nor needed for reasoning within
this context. Also, it's usually the case that much larger classes,
relationships, etc. are not mentioned or needed within this context.
- Those first two sub-dimensions23 can be thought of as asking the
question "What distinctions matter?" A different sort of
sub-dimension arises from asking the question "What phenomena matter?"
For example, does friction matter, do relativistic effects matter,
does weather matter, etc.?
- The final sub-dimension23 here has to do with representation systems
and abstract classes. It can be thought of as a sort of "Level of
formal entity" sub-dimension of Granularity.25 The context may assume
that the focal actors are at a certain level such as people,
corporations, countries; a book versus an edition of a book versus the
content of the book; a proposition or an entire theory or a
representation of one of those two in some language; particular versus
abstract game pieces; etc. Several real objects may embody one formal
object, such as several copies of Moby Dick being "the same book" at
some level of granularity, and different books at another level of
granularity. Or a certain chess game may be nothing more than an
abstract series of representations of moves at one level of
granularity, and, at another level of granularity, it might be an
actual event with specific physical players and pieces and movements.
Let's consider one simple example of Granularity, taken from the
current Cyc KB. The assertion that the mainland USA
(#$ContiguousUnitedStates) is #$spatiallyContinuous is asserted to be
true in the #$UnitedStatesGeographyMt context. But what about all the
small islands, sandbars, etc. just off the coast - such as Catalina
Island off the coast of southern California? They are considered part
of the contiguous 48 US States - they're part of the USA and not part
of Alaska or Hawaii - but on the other hand they are clearly not
spatially continuous with the rest of the mainland. The solution: the
spatial granularity of the #$UnitedStatesGeographyMt context is larger
(coarser) than any context in which those sandbars, islands, etc. are
known about. In that context, they don't even exist. The
#$UnitedStatesGeographyMt is talking about geographic regions that are
state-sized (or larger), not small-island-sized (or smaller). That
could be stated as a predicated domain-assumption of that context, but
having the Granularity dimension enables us to state it succinctly as
a Granularity value - i.e., that is one of the n "coordinates" of that
context that situate it in a region of the n-dimensional context
space.
The Granularity dimension is where we will integrate "order of
magnitude" reasoning into Cyc. E.g., so Cyc won't worry about quantum
wave phenomena when reasoning about the likely outcomes of a monster
truck pull.
Here is how this is represented in Cyc: we use these 6 new binary
predicates:
(#$mtLinearDistanceValue C INTERVAL) means that when reasoning in (or
with) the context C, spatial objects for which the longest axis
(longest linear dimension) falls within the range specified by the
#$Distance INTERVAL should be attended to, or taken into account, and
those which are much larger or smaller shouldn't. For example,
(#$mtLinearDistanceValue #$SleepMt (#$Meter .001 10)) means that when
reasoning about sleeping, it's unusual for objects < 1mm or > 10m in
length to be relevant.
(#$mtVolumeValue C INTERVAL) means that when reasoning in (or with)
the context C, spatial objects with a volume that falls within the
range specified by INTERVAL should be attended to, or taken into
account, but not those with larger or smaller volumes. For example,
(#$mtVolumeValue C (#$CubicMeter 1 100)) means that when reasoning
proceeds using the knowledge in C, only objects having a volume that
measures greater than or equal to 1 cubic meter, and less than or
equal to 100 cubic meters, should be considered relevant. Note: these
3 distance/area/volume predicates are weakly interdependent on each
other; if 1 or 2 are unspecified, they can be guessed from the 3rd.
(#$mtAreaValue C INTERVAL) means that when reasoning in (or with) the
context C, only objects with an area that falls within the range
specified by INTERVAL need be attended to, or taken into account. For
example, to indicate this value for one of the Geography contexts,
namely the one that has maps, distances, etc. from the 1995 CIA World
Fact Book, saying it dealt with areas between 10 and 100k square
miles, we'd write:
(#$mtAreaValue #$CIAWorldFactBook1995GeographyMt (#$SquareMile 10
100000)).
(#$mtSubsetAbstractionLevel CTXT COL) means that when reasoning in (or
with) the context CTXT, (instances of) classes of objects at about the
level of abstraction indicated by the collection COL should be
attended to, or taken into account. If you consider the knowledge base
as a lattice of abstract concepts arranged in a hierarchical structure
via the subset/superset relation (#$genls), then the further away (up
or down) in the hierarchy you go from COL, the less likely it is that
(instances of) those classes should be used in inferencing in context
CTXT. This is not symmetric, in that the fall-off of relevance is
likely to be much more pronounced and absolute in the "upward" (more
general) direction than the "downward" (more specific) direction.
Here is a related new predicate:
(#$mtPartonomicAbstractionLevel CTXT COL) is similar to the last
predicate. It means that when reasoning in (or with) the context
CTXT, (instances of) classes of objects at abou |