Re: SUO: Vote 2001-02: IFF Foundation Ontology
Robert,
One way to help show the relevance and accessibility of the IFF ontology
would be to give some examples of how to code the information expressed in
common English statements in IFF.
I did something similar in the series of "Hamlet" examples in the
message copied below, as well as the dialog with Josiane Caron-Pargue also
copied below.
Adam
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>Date: Tue, 29 May 2001 16:23:40 -0700
>To: Josiane Caron-Pargue <Josiane.Caron@mshs.univ-poitiers.fr>,
> standard-upper-ontology@majordomo.ieee.org
>From: Adam Pease <apease@ks.teknowledge.com>
>Subject: Re: SUO: olivier, tral 2, protocol
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>
>Josiane,
> I think we may not be communicating completely. I agree that the
> context of each sentence is different, but the semantics of the relation
> "on" seems the same in each.
> As an analogy, consider the following two sentences
>
>>1. John ate the sandwich.
>>2. Sue ate the cheese sandwich before her meeting with John.
>>
>>The information contained in the two sentences is different but the
>>semantics of "ate" is the same. Similarly, in
>>
>>3. In Bob's dream, he intended to eat the unicorn.
>>
>>the semantics of "ate" are the same even though situation is hypothetical
>>etc.
>>
>>We may have different understandings of the word "semantics". I'm using
>>it relative to the translation to logic of these sentences and the
>>appearance of a term from an ontology to represent the meaning contained
>>in the sentence. So, to translate these sentences, we might have the following
>>
>>1. (exists (?X)
>> (and
>> (instance-of ?X EatingEvent)
>> (performedBy ?X John)))
>>
>>2. (exists (?X ?Y ?Z)
>> (and
>> (instance-of ?X EatingEvent)
>> (performedBy ?X Sue)
>> (instance-of ?Z Sandwich)
>> (containsSubstance ?Z Cheese)
>> (objectDestroyed ?X ?Z)
>> (instance-of ?Y MeetingEvent)
>> (participant ?Y Sue)
>> (participant ?Y John)
>> (before ?X ?Y))
>>
>>3. (exists (?X)
>> (and
>> (instance-of ?X Dream)
>> (author ?X Bob)
>> (containsInformation ?X
>> (exists (?Y ?Z)
>> (and
>> (instance-of ?Y EatingEvent)
>> (instance-of ?Z Unicorn)
>> (goal Bob ?Y)
>> (performedBy ?Y Bob)
>> (objectDestroyed ?Y ?Z))))))
>>
>>In each of these formulas, the same term from an ontology "EatingEvent"
>>is used.
>>
>>Now, it occurs to me that you may have had a different point, which is
>>that "on" refers to a slightly different spatial relation in some of the
>>utterances below. A box may be "on" another box. A box may also be "on"
>>a boat but that use of "on" actually means "contained in". We might also
>>envision a carnival "ring toss" game in which a ring may be "on" a peg
>>although it really is surrounding the peg. Similarly, I may put "on" a
>>shirt which really means that it completely surrounds my torso.
>>
>>As a diversion, I'm trying to learn a bit of the Philippino language
>>Tagalog in preparation for a trip there. Tagalog has a very general
>>preposition "sa" which can variously mean "on", "to", "towards", and "on
>>top of". This relates to an earlier discussion about how natural
>>languages can lead us astray when it comes to creating good
>>ontologies. We must be careful to separate ontology and language as
>>there are many concepts which are needed in any rich ontology which don't
>>correspond directly to any one word in a human language.
>>
>>Do either of the two points above address the issue you're getting at?
>>
>>Adam
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>Date: Wed, 13 Jun 2001 13:38:54 -0700
>To: standard-upper-ontology@ieee.org
>From: Adam Pease <apease@ks.teknowledge.com>
>Subject: SUO: semiotics in SUO
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>
>Folks,
> We had some discussion a few months back about how to represent and
>relate informational content of books and performances. Ian and I
>discussed this topic again, relative to the semiotics terms he sent out to
>the list recently. The examples I suggested below can now be formalized
>as follows
>
>Hamlet the fictional character
>(instance-of Hamlet Human)
>
>Hamlet an edition of the printed play
>(subclass-of Hamlet-FolgerEdition ContentBearingObject)
>(subclass-of Hamlet-ScribnerEdition Hamlet-FolgerEdition)
>(equivalentContentClass Hamlet-ScribnerEdition Hamlet-FolgerEdition)
>(instance-of Hamlet-ScribnerEditionOnMyBookshelf Hamlet-ScribnerEdition)
>(containsInformation Hamlet-ScribnerEditionOnMyBookshelf Hamlet-ThePlay)
>
>A performance of Hamlet
>(instance-of HamletPerformanceByRoyalShakespeareCompanyOnJune18-2000
>Activity)
>(instance-of HamletPerformanceByRoyalShakespeareCompanyOnJune18-2000
>ContentBearingProcess)
>(realization-of HamletPerformanceByRoyalShakespeareCompanyOnJune18-2000
>Hamlet-ThePlay)
>
>A performance of Hamlet captured on video and encoded as a bit stream
>(instance-of
>VideotapeOfHamletPerformanceByRoyalShakespeareCompanyOnJune18-2000
>ContentBearingObject)
>(refers-to
>VideotapeOfHamletPerformanceByRoyalShakespeareCompanyOnJune18-2000
>HamletPerformanceByRoyalShakespeareCompanyOnJune18-2000)
>(instance-of
>BitStreamOfHamletPerformanceByRoyalShakespeareCompanyOnJune18-2000
>ContentBearingPhysical)
>(equivalentContentInstance
>VideotapeOfHamletPerformanceByRoyalShakespeareCompanyOnJune18-2000
>BitStreamOfHamletPerformanceByRoyalShakespeareCompanyOnJune18-2000)
>
>The text of Hamlet as character strings
>(subclass-of Hamlet-CharacterStrings ContentBearingObject)
>
>What Fritz Lehmann has called a "conceptual work" - the timeless
>informational content of the play
>(instance-of Hamlet-ThePlay Proposition)
>
>Note that these examples suggest four new semiotics notions, which can be
>defined as follows:
>
>(subclass-of Representation Physical)
>(documentation Representation "An instance of &%Physical that
>&%represents something else. Note that this is an intentional relation -
>instances of &%Physical that accidentally convey some meaning to an &%Agent
>would not be examples of &%Representations.")
>
>(=>
> (instance-of ?OBJ Representation)
> (exists (?ENTITY)
> (represents ?OBJ ?ENTITY)))
>
>(subclass-of ContentBearingProcess Representation)
>(relatedInternalConcept ContentBearingObject realization-of)
>(documentation ContentBearingProcess "Any &%Process that expresses a
>&%Proposition. It is important to distinguish &%Propositions from the
>&%ContentBearingProcesses that express them. A &%Proposition is a piece of
>information, e.g. that the cat is on the mat, but a &%ContentBearingProcess
>is
>an &%Process that realizes this information. A &%Proposition is an
>abstraction
>that may have multiple representations: performances, sounds, bit streams,
>etc.")
>
>(=>
> (instance-of ?PROCESS ContentBearingProcess)
> (exists (?PROP)
> (realization-of ?PROCESS ?PROP)))
>
>(subrelation-of equivalentContentInstance subsumesContentInstance)
>(instance-of equivalentContentInstance EquivalenceRelation)
>(nth-domain equivalentContentInstance 1 Representation)
>(nth-domain equivalentContentInstance 2 Representation)
>(documentation equivalentContentInstance "A binary relation between two
>instances of Representation. '(equivalentContent ?OBJ1 ?OBJ2)' means that
>the content expressed by ?OBJ1 is identical with the content expressed by
>?OBJ2. An example would be the relationship between a handwritten draft of
>a letter to my lawyer and a typed copy of the same letter. Note that
>'(equivalentContentInstance ?OBJ1 ?OBJ2)' implies '(subsumesContent ?OBJ1
>?OBJ2)' and '(subsumesContent ?OBJ2 ?OBJ2)'.")
>
>(instance-of subsumesContentInstance PartialOrderingRelation)
>(nth-domain subsumesContentInstance 1 Representation)
>(nth-domain subsumesContentInstance 2 Representation)
>(documentation subsumesContent "A binary relation between two instances of
>Representation. '(subsumesContent ?OBJ1 ?OBJ2)' means that the content
>expressed by ?OBJ1 contains the content expressed by ?OBJ2. An example is
>the relationship between a handwritten poem and one of its stanzas. Note
>that this is a relation between instances of Representation, rather than
>Classes. If one wants to assert a relationship between Classes, e.g.
>between the edition of a particular work and a part of that work, the
>relation subsumesContent should be used.")
>
>(=>
> (and
> (subsumesContentInstance ?OBJ1 ?OBJ2)
> (subsumesContentInstance ?OBJ2 ?OBJ1))
> (equivalentContentInstance ?OBJ1 ?OBJ2))
>
>(=>
> (subsumesContentInstance ?OBJ1 ?OBJ2)
> (forall (?INFO)
> (=>
> (containsInformation ?OBJ1 ?INFO)
> (containsInformation ?OBJ2 ?INFO))))
>
>What are everyone's thoughts on this?
>
>Adam
At 11:54 AM 8/16/2001 -0700, Robert E. Kent wrote:
>John,
>
>I more or less agree with you (see comments below).
>
> > I am sympathetic to the use of category theory as a framework for
> > supporting the multiple mappings between various theories in the
> > infinite lattice. However, I agree with you that the terminology
> > of category theory is unfamiliar even to most mathematicians and
> > logicians, and it generally strikes terror in the hearts of everyone
> > else.
>
>See the brief technical discussion below on truth concept lattices (the
>"infinite lattice") and 1st-order interpretations (the "multiple mappings
>between various theories").
>
> > I believe that the appropriate place for category theory is under
> > the rug where no one will ever see it.
>
>The "no one" here is too strong.
>
>In the programming language analogy that I made in the document
>[http://suo.ieee.org/Kent-IFF.pdf], users of software applications should
>not
>see the source code, but the programmers of those applications need to have
>it visible in front of them. In the IFF approach certain people working in
>certain roles will need to see and use the IFF Category Theory Ontology,
>whereas others will want it to be invisible. See the further comments below
>on role types and visibility.
>
> > It would be useful to have
> > a white paper that shows how all the mappings from theory to theory
> > can be untangled in category land, but then present the results
> > without using any of the terminology of category theory.
>
>Thanks for the suggestion. I volunteer to help write such a white paper. See
>further comments below on the truth concept lattices and maps between them.
>
> > No one
> > who uses the ontology (even with the lattice of theories is shown
> > right up front) should ever see any of the terminology or machinery
> > of category theory.
>
>I agree. Note the word "uses". See further comments below on role types and
>visibility.
>____________________________________________________________
>____________________________________________________________
>
>I. Discussion of role types and visibility of IFF terminology and
>axiomatizations:
>
>As I mention in a previous message
>[http://suo.ieee.org/email/msg05907.html], the IFF is partitioned into three
>levels (object level, lower metalevel, upper metalevel), and the visibility
>of these levels depends upon the role that people play with respect to the
>IFF:
>__________
>
>There were comments and concerns at the SUO workshop about intimidating
>users with category theory terminology. But as I commented at the workshop,
>and have repeated above, the terminology visible to the user is that
>introduced in the domain ontologies, and the foundation terminology visible
>to the content ontology developer is that terminology introduced in the
>lower metalevel -- terms such as 'subtype', 'expression', 'model',
>'1st-order interpretation', etc. This is normal semantic terminology, but
>not category theory terminology. The category terminology is introduced in
>the upper metalevel, and this is seen only by the lower metalevel. Compare
>the dependencies in Figure 1 "IFF Foundation Ontology (with dependencies)"
>of the document [http://suo.ieee.org/Kent-IFF.pdf].
>__________
>
>Here I expand on that discussion of role types and ontological visibility.
>
>There are two distinctions concerned:
>
>A. designer versus user
>
>B. 3 levels of terminology:
>object level, lower metalevel, upper metalevel
>
>Note: a designer must do some reasoning about the module being developed.
>
>These two distinctions are combined into six possible role types, of which
>we identify two pairs, ending up with four possible distinct role types. The
>first two role types do not want to see category theory terminology -- they
>want it swept under the rug. However, the second two role types need to
>use category theory terminology.
>
>1. object level user
>
>A person in this role (with respect to the IFF) sees only object level
>terminology, that is, they see only domain/middle/upper ontology
>terminology.
>
>Example terminology:
>
>a. From a Movie domain ontology:
>'movie', 'actor', 'rating' ...
>
>b. From an upper object level ontology
>'3D', '4D', 'object', 'event', 'continuant', 'occurrent', ...
>
>2. object level module designer = lower metalevel user
>
>A person in this role (with respect to the IFF) sees both object level and
>lower metalevel (model theory) terminology.
>
>Example terminology:
>
>a. From the IFF Model Theory Ontology:
>'instance', 'type', 'classification', 'expression', 'arity', 'sentence',
>'language', 'model', 'satisfies', '1st-order interpretation' ...
>
>===========================================
>visibility boundary for category theory terminology (John's "rug")
>===========================================
>
>3. metalevel module designer = upper metalevel user
>
>A person in this role (with respect to the IFF) sees both lower metalevel
>(model theory) and upper metalevel (core and category theory) terminology.
>
>Example terminology:
>
>a. From the IFF Model Theory Ontology:
>'instance', 'type', 'classification', 'expression', 'arity', 'sentence',
>'language', 'model', 'satisfies', '1st-order interpretation' ...
>
>b. From the IFF Core Ontology:
>'class', 'function', 'relation', 'complete-lattice', 'concept-lattice', ...
>
>c. From the IFF Category Theory Ontology:
>'category', 'functor', 'pullback', 'colimit', 'monad', ...
>
>4. upper metalevel designer
>(myself, as designer of the IFF upper metalevel, and other
>category-theorists that might help in the future)
>
>A person in this role (with respect to the IFF) sees only the upper
>metalevel (core and category theory) terminology.
>
>Example terminology:
>
>a. From the IFF Core Ontology:
>'class', 'function', 'relation', 'complete-lattice', 'concept-lattice', ...
>
>b. From the IFF Category Theory Ontology:
>'category', 'functor', 'pullback', 'colimit', 'monad', ...
>____________________________________________________________
>____________________________________________________________
>
>II. Discussion of truth concept lattices and 1st-order interpretations
>(somewhat technical!).
>
>The *truth classification* was discussed as example 4.6 on page 71 of the
>book "Information Flow: The Logic of Distributed Systems" by Jon Barwise and
>Jerry Seligman. I have introduced its concept lattice which I call the
>*truth concept lattice*, and illustrated this on slides 5 and 6 of my SUO
>Workshop PowerPoint presentation
>[http://reliant.teknowledge.com/IJCAI01/Kent.ppt]. The truth classification
>and truth concept lattice occur as examples within the IFF Core
>(sub)Ontology of version 2.0 of the IFF Foundation Ontology (to be submitted
>to SUO next month). Amongst other things, the axiomatization of large
>concept lattices in version 2.0 answers Chris Menzel's foundational concerns
>about a "reasonable class theory" mentioned in the message
>[http://grouper.ieee.org/groups/suo/email/msg01759.html].
>
>The first thing to note is that we are dealing with a fibered structure
>here. I have proposed that the truth concept lattice be used in SUO as John
>Sowa's potentially infinite open-ended lattice of theories. However, there
>is no single lattice here but an infinite collection of lattices, where each
>truth classification "truth-classification(L)" and each truth concept
>lattice "truth-lattice(L)" is based upon (indexed by) a particular 1st-order
>language L. So a particular object level ontology -- be it a domain
>ontology, a middle level ontology, or an upper level ontology -- will be an
>element of a lattice based on its 1st-order language. Internally, the
>various ontologies (theories) are connected by generalization/specialization
>and sideways jumping. Externally, the lattices in the IFF framework are
>connected in many different ways, such as by the FCA notions of apposition
>and subposition, etc. But a very special and especially interesting
>connection is through 1st-order interpretations.
>
>The notion of a *1st-order interpretation* was discussed as example 4.11 on
>page 74 of the book by Jon Barwise and Jerry Seligman [op. cit.]. 1st-order
>interpretations are axiomatized in the IFF Model Theory Ontology module of
>the IFF Foundation Ontology (to be submitted to SUO sometime later this
>fall). A 1st-order interpretation I : L1 -> L2 from one 1st-order language
>L1 to a second 1st-order language L2 maps the relations of L1 to the
>formulas of L2. For us here, there are two relevant passages:
> 1st order interpretation
> |=> infomorphism between truth classifications
> |=> adjoint pair between truth concept lattices
>Each 1st-order interpretation
>I : L1 -> L2
>defines a "truth infomorphism" between the associated truth classifications,
>truth-classification(I) : truth-classification(L1) ->
>truth-classification(L2)
>(see Barwise and Seligman [op. cit.]). And this infomorphism defines an
>"truth adjoint-pair" (of monotonic functions) between the associated
>truth concept lattices,
>truth-adjoint-pair(I) : truth-lattice(L1) -> truth-lattice(L2)
>(axiomatized in the IFF Model Theory Ontology). Now, these monotonic
>functions map between formal truth concepts (that is, ontologies) in a very
>semantic way.
>____________________________________________________________
>____________________________________________________________
>
>Robert E. Kent
>rekent@ontologos.org
Adam Pease
Teknowledge
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