RE: SUO: RE: More KIF-ified Ontology Content
Patrick - Thanks for your comments on my message, which are an
excellent statement of an attitude towards the SUO which I think is
woefully overoptimistic. I would take too long to go into full detail
- that would be a book-length reply - but I will try to elaborate on
my points in response, to clarify why I think the vision you have in
mind is unworkable and indeed almost certainly impossible to achieve,
and give some examples.
>Pat --
> My understanding of the purpose (or one purpose) of the SUO
>effort was to create a defining vocabulary of basic terms that will
>allow a user to define a concept in terms of the SUO and thereby
>permit someone with a different ontology to use the same concept,
>with the same axioms and inferences, when two ontologies want
>to transfer information.
Already this seems odd. If they are using the same axioms and
inferences, then in what sense are the ontologies different? An
ontology only is a set of axioms. The key point is that different
ontologies will not use the same axioms, not even the same nonlogical
vocabulary, and that the various vocabularies in use will be (and
already are) profoundly irreconcilable with each other.
> What this requires is a set of basic
>concepts that will allow differing perspectives on the same issue to
>be represented, and allow differing perspectives to be recognized as such.
That would indeed be a noble ambition, but that is not a standard
ontology, but a kind of meta-ontology interaction mechanism. The
difference is like trying to automate machine translation, instead of
trying to invent SU-Esperanto.
> Your point, as I understand it, has been asserted previously:
>
> > My point was that there isnt going to be (for the
> > reasons which Chris outlined so cogently in his original message) one
> > Good Enough Ontology, if 'good enough' means that it will accomodate
> > all ontological perspectives reasonably well. You seem to think that
> > this is like choosing a standard notation, but it's more like taking
> > a definite position on every deep question in philosophical analysis
> > for the last two thousand years, and declaring that particular
> > combination of philosophical perspectives to be 'good enough' for
> > everyone to use for any reasonable purpose. Why do you think that
> > people have been arguing about this for so long, if they felt that
> > one or another position was 'good enough'?
>
> The question, whether one defining vocabulary can be found to
>express any chosen perspective, does not require that every perspective be
>accepted as true in the basic ontology. A standard upper ontology can
>be used to define many incompatible "possible worlds", which, if properly
>documented, will be recognized as incompatible.
What sense of 'incompatible' are you using here? In my sense, they
are in contradiction with one another, so if they are to coexist, one
needs something other than a logic to express them in.
>We can define Newtonian
>and relativistic mechanics using the same language -- that's my hope for
>the SUO.
If I may say so, that is a very bad illustration, since in fact one
*cannot* express relativity in a Newtonian framework. "energy",
"space" and "time" all have different meanings in relativistic
kinematics. The languages might LOOK the same, but they arent the
same, because the meanings have changed.
> The question your comment raises is whether there are some pairs
>of concepts so fundamentally different that no common set of defining axioms
>
>can serve to define both.
Yes; in fact, I will claim that if you take two concepts at random
from two different ontologies, there is a good chance that they will
be fundamentally incommensurate in meaning. In other words, this is
the norm, not the exception.
>If we define both time points and time intervals,
>and allow the users to decide which representation of time is best for
>their applications, will any logical contradictions occur within the
>defining vocabulary?
Yes, immediately. If you are not careful, you will get dozens of
contradictions. (Which sense of 'interval' do you mean? Allen's
temporal ontology uses a sense different from that used in topology
and analysis, mereology uses yet another different notion, and
temporal databases yet another.) Probably about 50 person-years have
been spent on this topic of time-intervals. If you manage to get
space sorted out, write it up and publish it immediately.
>More generally, it would be very important to
>have examples of differing viewpoints that appear to be so
>fundamentally different that no basic set of axioms can define both.
My old time catalog gives about 10 such incommensurate theories for
time-intervals and points. As most such pairings are like this, let
me turn the challenge around and ask you to find me some which are
such that a single set of axioms CAN characterise them both.
>If you could provide some examples of such incompatible concepts it
>would be a great help in clarifying the fundamental issue we have to
>deal with.
>
> To consider one of your specific questions:
>
> > Do the axioms refer to things which endure through time, and
> > consider these a fundamentally different kind of entity than things
> > which happen at a time? Do they assume that truths are asserted at a
> > time (and hence are implicitly or explicitly tensed) or are the
> > assertions themselves timeless, and asserted about temporally located
> > things?
> Certainly, axioms serving as assertions about specific material
>objects in space-time till be time-dependent, but axioms used for
>defining classes of concepts by their relation to other objects will not
>necessarily be time-dependent.
OK, that's one of my possible answers. However this is highly
controversial, as it results in a temporal ontology which uses
tenses. I, for one, won't use this, and will continue to write axioms
about four-dimensional 'worms' (in Fritz Lehman's terminology). It is
also incompatible with CYC and most temporal databases. Care to try
again?
>The axioms might look very similar
>in many cases, except for an explicit time point or time interval
>in assertions about objects in the real world.
How will you compare properties of the same thing at different times
(as in "I seem to weigh more than I used to")?
>Is there some
>logical contradiction in believing that we can have both time-
>independent definitional axioms and time-dependent assertional
>axioms?
No contradiction there, but it isnt really workable in practice: much
too restrictive.
> > When the properties of something change with time, does one
> > indicate this by referring to the time at which they hold, or does
> > one regard the relations and properties as holding of temporal
> > 'slices' of the things, or does one refer to the changes explicitly?
>
> Do you think it is impossible to create one set of defining concepts
>that will allow a user to assert facts using any one of these methods,
>as seems best suited for the task?
Yes, because the consequences of this decision have far-reaching
effects on the entire ontology, since they impose different axiomatic
styles. To say that cat sat on the mat, does one write
SatOn(Cat, Mat, t) or
SatOn(Cat@t, Mat@t) or
TrueAt(SatOn(Cat, Mat),t), or just
SatOn(Cat, Mat) with some meta-assertion about when this 'holds', or
what? You can't have it all ways: you have to choose a language and a
notation, and whatever you choose will have set some controversial
ontological decisions in stone.
BTW, you could also decide to say something like
(exists (?x)(sitting-event(?x) and agent(?x, Cat) and placeOf(?x,
Mat) and Timeof(?x, t)))
or maybe introduce temporally-flagged 'properties' called 'sittings'
and apply one to the cat, or..... I could go on, but you probably get
the point.
(If you are going to suggest that we allow all of these, then
consider what happens when they get mixed up. If I can use all this
notation in one ontological framework, then I can write things like
TrueAt(SatOn(Cat@t1, Mat, t2),t3), which don't mean anything coherent
at all. Thats what I meant by a 'muddle' in an earlier message. )
> It can be anticipated that different users might well create
>different ontologies in which the axioms are contradictory. This is
>unavoidable with any defining vocabulary -- one user says "yes" when
>another says "no".
Thats not the issue I'm focussing on. What about the case where both
say YES, and they even seem to agree, but in fact they are making
contradictory hidden assumptions.
For example, thre are a number of mereotopological ontologies for
spatial reasoning out there in the wide world. Typically they have
relations of 'being part of' and 'being adjacent' which hold between
pieces of space, and axioms like the 'proper part axiom' which says
that if X is a part of Y and not identical to it, there there is some
other thing Z which is also part of Y but shares no part with (doesnt
overlap) X. Sounds reasonable, right? But if you wrote this axiom out
in logic, you will be using quantifiers, and there is an implicit
assumption that these quantifiers range over a certain kind of piece
of space: basically, what topology calls regular sets, which roughly
are 'fat' pieces of space, but not things like points, lines or
surfaces. But what if you want to talk about lines sand surfaces?
Just add them to the ontology, right? Wrong. Because if you do, all
those mereotopology axioms will immediately not be true any more,
since they assumed (without actually SAYING this, since there was no
need to do so) that when they said 'forall...' they DIDNT mean things
like this. Just by adding a new category, you have 'spoiled' all the
quantifiers in the mereotopology axioms.
OK, this can be fixed by rewriting all those axioms with the
restriction to 'fat' pieces of space made explicit (provided of
course you know how to characterise them somehow, which is new
ontological work since its impossible to do so in mereotopology,
since it just assumes everything is like that). Im not saying this
can't be done, but I am saying that (1) it needs to be done almost
every time you add two ontologies together (2) it cant be done in
advance, since you cant tell in advance what new conceptual
extensions to the universe someone else is going to add later and (3)
it can't be done by magic: its going to require hard, applied,
expensive effort, each time.
The SUO dream is that this work can be done once, and never done
again, but it can't; except by imposing an universal ontology which
has all the distinctions pre-made and catalogued, which is just a way
of saying that it is forbidden to do add anything new. But that's
not an SUO, its an SO, like Cyc.
>The function of the SUO in such cases is to
>point out the differing definitions used for similar objects, which
>will allow one system to adjust its reasoning about objects defined
>in other ontologies, and in favorable cases to recognize the different
>inferences that the other system must generate using its different
>definitions. With a common defining vocabulary, there is a mechanism
>to allow correct inferences can be drawn (provided the two systems
>exchange their definition set), and without a common vocabulary the
>chances may be nil in many cases.
There is no common defining vocabulary. As soon as you write a
quantifier, you have made some assumptions about the universe which
someone else might want to disagree with.
> > Some things are easier to say in some ways than others; some
> > things are unsayable in some combinations of answers, but those
> > combinations are recommended by weighty ontological authorities armed
> > with truckloads of scholarship, so you are going to have some mighty
> > battles ahead. (Guarino agrees with Aristotle that all events
> > ultimately derive from enduring continuants; other living
> > philosophers agree with Heraclitus that the primary mode of existence
> > is flux, so things supervene on events. People will still be arguing
> > about this two millenia from now. Practical folk use whichever
> > viewpoint is handiest, but then they don't have to be logically
> > consistent.)
> The SUO goal is to find the most basic logical vocabulary in which
>everything
>is "sayable".
To repeat, there is no such basic vocabulary.
>You seem to have no trouble describing the differences above
>in English. My belief is that if something can be defined in English, it
>can be defined in a logical language -- provided that it is meaningful,
>and the English is unambiguous in its intended context.
I guess my only response to this is to smile at your naive optimism.
Sorry to seem offensive, but have you ever read anything about
meaning in NL? Just take a look at spatial prepositions, for a start.
There are several hundred distinct senses (Melissa Bowerman has them
catalogued) made by some human language, and every language uses only
about a dozen words to indicate them all. The English word "on" has
over 50 meanings. People havnt even got a universally agreed-on
specification of English syntax, let alone English meanings.
> > Whatever you decide, you had better get it done soon, as
> > most of these files of axioms being produced will need to be entirely
> > re-written, since every author writes axioms based on their own
> > idiosyncratic answers to these (and other) questions, and their
> > particular assumptions are built into their very way of thinking, and
> > not made explicit, but are inconsistent with other author's implicit
> > answers.
> Here I strongly agree. We need to work top-down to create the
>defining vocabulary for the most basic concepts, and use those to
>create more complex concepts, and so on. The temptation is to try the
>more interesting middle-level concepts first, which has the risk you
>point out.
Actually I think this is probably the most constructive strategy,
since there isnt much that can be usefully said about the very
high-level concepts.
> > Guarino's mereology isnt compatible with Simon's, and neither of them
> > are compatible with Tarski (last time I looked), so y'all had better
> > decide which you want to believe. Most of the mereological accounts
> > of space do not allow things like lines, surfaces or points to occur
> > in the domain of discourse, and rapidly generate inconsistencies if
> > they are allowed in, so you had better not meet anyone who wants to
> > talk about the length or shape of a boundary line.
> If others agree that the goal of an SUO is to allow anything to be
>defined, then we need to accommodate lines and points and open and closed
>intervals as well as regions of space.
By using the term 'open and closed intervals' you have already made
a major ontological committment (to thinking of intervals as sets of
points) which agrees with modern mathematical practice, but is
incompatible with most of mereology (including some of the axioms you
already have in the SUO, by the way) and also with the temporal
ontologies used in for example qualitative reasoning.
It is almost impossible to say anything without making an ontological
committment that someone else will disagree with (and for good
reasons).
> If someone wants to define
>some concepts without using lines or points, those concepts should still
>be very well-formed and well-defined. If inferences on the objects
>defined in that way differ from those using points and lines, then
>the users need to be aware of the differences and choose the
>representation that provides the reasoning power they need.
There isnt even ontological agreement on what points and lines *are*.
> > (Check the Cyc geography axioms pretty carefully, and be prepared to
> > re-think them one at a time;
> Do you think there are logical inconsistencies in the CYC base KB?
>(I think there are gaps that need filling, but that's a different
>question).
Probably, but that wasnt my point: it was that the Cyc axioms depend
on the use of concepts which are ontologically distinct from those
used in mereotopology.
> > Holes require something like pieces of space in the ontology. . . .
> One might find that different people want to define holes
>or some other concepts differently. The SUO should provide the vocabulary
>for any definition, but if there is a serious difference of opinion,
>multiple distinguishable definitions (with different names) can be
>provided, and SUO should not require that any one definition be used.
>
> > (For example, Cyc doesnt make any firm distinction between a thing
> > and the space it occupies, whereas most mereologies make a very sharp
> > distinction.)
> There may be cases where some choices have to be made in the SUO --
>certainly distinguishing between a region of space and the matter
>that occupies it is likely to be one of them. But does CYC really
>fail to make any distinction? That doesn't seem to follow from the
>fragment of CYC available publicly -- is it in there and I missed it, or
>is it something embedded in the unavailable reasoning mechanisms?
Check out the explanation of "SpatialThing" and "Near". But to be
fair to the Cyc developers, I know they are in the process of
clearing this oddity up and rewriting the spatial concepts in Cyc to
be conceptually closer to the more common view (partly spurred on by
all the awkward questions we asked them :-)
> > There isnt going to be a single UO which allows them
> > all to coexist, and if you try to take a bit from one and a bit from
> > another you will just get incoherence and muddle.
> If one views the SUO as some set of assertions about the real world
>we live in, it does seem likely that there will be incompatible theories.
>But if it is considered to be the logical language that can describe the
>real world,
The logical language is SUO-KIF. I agree that can be well-defined and
standardised reeasonably successfully, but that is entirely beside my
point.
> with enough well-defined content referencing objects in the
>real world so that it is not merely a set of symbols, then it is not
>immediately obvious that it will not be able to represent all reasonable
>theories about the real world. Mass, time (what we measure on clocks),
>and meter are well-defined and provide a grounding for the other
>definitional symbols. Where there are gaps, new concepts can be defined.
>If some new concepts are logically incompatible with existing content,
>existing content can be changed to allow defining both old and new
>concepts.
Well, you can hope and pray that will be the case, but the evidence
is against you, it seems to me. Do you have any *reason* for this
optimism?
> We can hope that this latter necessity will become rare
>as the SUO matures.
You can hope, indeed.
>
> > There isnt a single
> > 'reasonably general and correct' ontology: there are many ontologies,
> > all general and all with as valid a claim to be 'reasonable and
> > correct' as all the others, but sharply incompatible with each other.
> > Some ambitious folk want their ontology to include a distinct entity
> > for every fact that can be asserted in the language (Jerry Hobbs
> > calls these 'eventualities'), which is going to be inconsistent with
> > any SUO that anyone produces.
> Is it possible to define eventualities without mandating their
>usage? I am unfamiliar with this aspect of Hobbs's work. Certainly
>there should be no problem in contemplating many individual instances
>of the concept "assertion" -- but I presume this is a different matter.
Different but closely related. Here is Hobb's idea, in his own words:
> > p(x) says that p is
> >true of x. p'(e,x) says that e is the situation or eventuality of p
> >being true of x. The relation between p and p' is given by the axiom
> >schema
> >
> > (A x)[p(x) <--> (E e)[p'(e,x) & Rexists(e)]]
> >
> >I.e., p is true of x iff there is an eventuality e that is p's being
> >true of x and e exists in the real world.
The use of the 'prime' on p here is a notational trick to associate
the eventuality-relation with the original predication. But
notational quibbles aside, Hobbs' ontological idea is that there is a
real entity corresponding to every assertable proposition. Its not
the same as the proposition (it's not true or false, for example) but
it does exist; in fact, his worlds are *made* of these things, like a
kind of tangle of propositional taffeta. They don't have what we
would call physical objects in them at all, only eventualities of the
existence of physical objects; the objects themselves are more like
platonic ideals. Now, could the SUO accomodate this degree of
ontological promiscuity (as Jerry calls it)? For the record, I don't
like this ontology, but many people do. Ideas like this are not as
alien for people working in computational linguistics.
> > So, in spite of your protests, you ARE
> > going to have to decide on a one true ontology, or at any rate a one
> > standard ontology; and if that word "standard" is going to have any
> > real meaning, then it might as well be written "true", since
> > obviously the point here is to say that you can have any ontological
> > color as long as it's black.
> >
> Not necessarily "absolutely true" but useful enough to be valuable,
>for all those whose theories are definable in SUO terms, which
>may eventually be almost everyone.
I can guarantee it will not be everyone. It may be almost no-one, is
the possibility you should consider carefully.
> >
> > PS. [Actually an alternative strategy would be to explicitly include
> > all the alternatives into the SUO, using some kind of 'context'
> > mechanism, maybe (?) To be really useful however this would need to
> > be more powerful than the 'micro-theory' notion used in Cyc, which is
> > really only a namespace-management tool. You would want to have
> > axioms relating the various notions of 'part' in different
> > ontologies, or the various ways of referring to time and change, in
> > the form of mappings between contexts. It would go way beyond
> > SUO-KIF, for sure.]
> >
> The SUO itself should not contain logically incompatible axioms,
>but when assertions are made about objects in the real world,
>contradictions can be readily generated. If there are incompatible
>Microtheories that are all useful, they could be maintained as
>extensions to the SUO.
> Once again, examples of concepts that simply can't both be defined with
>the
>same set of basic concepts will be very helpful.
I have given you several above. Almost any pair of distinct
nontrivial ontologies cannot be so defined (or at least not without
major intellectual effort which has not yet been done). I would
challenge you to give a single example where such common definitional
bases are known to exist.
> The examples you have
>given thus far seem to mostly address the inconsistent content of
>differing definitions of the same word or assertions about the real world,
>and it isn't clear that in these examples you mean to assert that the
>different representations can't use the same logical language.
They can all use the same *logical* language (well, if that includes
predications, in Hobbs' case), but they can't use the same nonlogical
vocabulary, or even the same ranges of quantification.
Pat Hayes
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