From weltyc at cs.vassar.edu Tue Jan 1 20:29:40 2002 From: weltyc at cs.vassar.edu (Christopher A. Welty) Date: Fri Oct 10 03:32:40 2003 Subject: KIF: Re: SUMO axiomatization In-Reply-To: <3C24D709.84BC63F1@bestweb.net> References: <3C24D709.84BC63F1@bestweb.net> Message-ID: Thanks for pointing this out, John. It brings up an interesting point for me - (sorry if this was discussed already during my SUO-absence) - do people find this to be "upper level"? Certainly if graphs is considered upper level, then this library demonstrates that there are over a hundred other things at the same "level". -Chris At 1:55 PM -0500 12/22/01, John F. Sowa wrote: >There is a collection of over a hundred mathematical theories >(fully axiomatized) that were developed to run under IMPS >(Interactive Mathematical Proof System). The theorem-proving >programs that use these axioms run on most versions of LISP and >are available from Mitre as software that has been made freely >available. Following is the home page: > > http://imps.mcmaster.ca/ > >The theories include graphs, groups, fields, automata, >and several versions of geometry, arithmetic, etc. > >MITRE has granted a public license for use of this material. >Following is the first paragraph: > > The MITRE Corporation (MITRE) provides this software to you without > charge to use, copy, modify or enhance for any legitimate purpose > provided you reproduce MITRE's copyright notice in any copy or > derivative work of this software. > >See the following file for the full license: > > http://imps.mcmaster.ca/imps-system/public-license > >Since MITRE has put very few restrictions on their license, they >would probably be amenable to making the software and axioms >available to the IEEE with any license modifications that the >IEEE might require. > >Suggestion: Rather than develop a new collection of mathematical >axioms for the SUO, which may or may not be consistent with IMPS, >I recommend that the SUO adopt the IMPS axioms from MITRE as the >basis for the mathematical modules in SUMO and other SUO projects. >Following are the reasons: > > 1. The IMPS axioms have been under development since 1990 and have > been tested in theorem-proving programs that have been used at > many universities and research institutions. That gives some > assurance that most, if not all, of the major bugs and problems > have been recognized and corrected. > > 2. The IMPS notation is based on a typed predicate calculus written > in a LISP-based notation, which should be fairly easy to translate > to KIF and other related versions of logic, such as CGs. > > 3. There is extensive documentation available on the IMPS web site, > including about two dozen published papers and technical reports. > Folllowing is the user's manual: > > http://imps.mcmaster.ca/manual/ > > Following are the more theoretical papers: > > http://imps.mcmaster.ca/doc/major-imps-papers.html > >John Sowa -- Christopher A. Welty http://www.cs.vassar.edu/faculty/welty/ Vassar College Computer Science Dept. Voice: (845) 437-5992 Poughkeepsie, NY 12604-0462 Fax: (845) 437-7498 From sowa at bestweb.net Tue Jan 1 21:27:31 2002 From: sowa at bestweb.net (John F. Sowa) Date: Fri Oct 10 03:32:40 2003 Subject: KIF: Re: SUMO axiomatization References: <3C24D709.84BC63F1@bestweb.net> Message-ID: <3C327E23.170946C@bestweb.net> Chris, I would include all mathematical structures under the category Abstract in my ontology. In fact, everything under that category is of the same nature as Abstract; i.e., it is the category of every kind of form that can be defined without contradiction. The subtype Schema includes all the "static" structures, and the subtype Script includes all the "dynamic" structures -- i.e., all those that have a time-like succession of forms. As Nicola keeps insisting, the category of abstractions is outside of space & time. That is true, but you can have mathematical theories that include a dimension labeled t, which just happens to be very time-like. "Christopher A. Welty" wrote: CW> Thanks for pointing this out, John. It brings up an interesting > point for me - (sorry if this was discussed already during my > SUO-absence) - do people find this to be "upper level"? Certainly if > graphs is considered upper level, then this library demonstrates that > there are over a hundred other things at the same "level". At 1:55 PM -0500 12/22/01, John F. Sowa wrote: JFS>There is a collection of over a hundred mathematical theories > >(fully axiomatized) that were developed to run under IMPS > >(Interactive Mathematical Proof System). The theorem-proving > >programs that use these axioms run on most versions of LISP and > >are available from Mitre as software that has been made freely > >available. Following is the home page: > > > > http://imps.mcmaster.ca/ > > > >The theories include graphs, groups, fields, automata, > >and several versions of geometry, arithmetic, etc. The category of all abstractions has forms for everything that exists and everything that might exist without contradiction in any kind of universe. So it is even richer than the category Physical, which only includes those kinds of things that are physically possible in our universe. All those theories can be organized in a lattice, according to the partial ordering defined by implication; i.e., if every axiom of theory A is a theorem of theory B, then A is more general than B. But not all mathematical theories are in the upper level. Chess, for example, is a mathematical theory, but it would be farther down the hierarchy. And I would also include the mathematical forms of virtual reality under the category of abstractions. For examples, see the following web site, which has a couple of frames from a recent movie. It took 90 minutes of time on a supercomputer to do all the computations for each frame: http://a330.g.akamai.net/7/330/2540/e15dfb847b2b87/www.e-insite.net/ednmag/contents/images/185947f6.pdf All the computer is doing is generating lots of colored polygons. Those polygons would be fairly far down the hierarchy, but they're still abstract. John From sowa at bestweb.net Tue Jan 1 21:27:31 2002 From: sowa at bestweb.net (John F. Sowa) Date: Fri Oct 10 03:32:41 2003 Subject: SUO: Re: KIF: Re: SUMO axiomatization References: <3C24D709.84BC63F1@bestweb.net> Message-ID: <3C327E23.170946C@bestweb.net> Chris, I would include all mathematical structures under the category Abstract in my ontology. In fact, everything under that category is of the same nature as Abstract; i.e., it is the category of every kind of form that can be defined without contradiction. The subtype Schema includes all the "static" structures, and the subtype Script includes all the "dynamic" structures -- i.e., all those that have a time-like succession of forms. As Nicola keeps insisting, the category of abstractions is outside of space & time. That is true, but you can have mathematical theories that include a dimension labeled t, which just happens to be very time-like. "Christopher A. Welty" wrote: CW> Thanks for pointing this out, John. It brings up an interesting > point for me - (sorry if this was discussed already during my > SUO-absence) - do people find this to be "upper level"? Certainly if > graphs is considered upper level, then this library demonstrates that > there are over a hundred other things at the same "level". At 1:55 PM -0500 12/22/01, John F. Sowa wrote: JFS>There is a collection of over a hundred mathematical theories > >(fully axiomatized) that were developed to run under IMPS > >(Interactive Mathematical Proof System). The theorem-proving > >programs that use these axioms run on most versions of LISP and > >are available from Mitre as software that has been made freely > >available. Following is the home page: > > > > http://imps.mcmaster.ca/ > > > >The theories include graphs, groups, fields, automata, > >and several versions of geometry, arithmetic, etc. The category of all abstractions has forms for everything that exists and everything that might exist without contradiction in any kind of universe. So it is even richer than the category Physical, which only includes those kinds of things that are physically possible in our universe. All those theories can be organized in a lattice, according to the partial ordering defined by implication; i.e., if every axiom of theory A is a theorem of theory B, then A is more general than B. But not all mathematical theories are in the upper level. Chess, for example, is a mathematical theory, but it would be farther down the hierarchy. And I would also include the mathematical forms of virtual reality under the category of abstractions. For examples, see the following web site, which has a couple of frames from a recent movie. It took 90 minutes of time on a supercomputer to do all the computations for each frame: http://a330.g.akamai.net/7/330/2540/e15dfb847b2b87/www.e-insite.net/ednmag/contents/images/185947f6.pdf All the computer is doing is generating lots of colored polygons. Those polygons would be fairly far down the hierarchy, but they're still abstract. John From graham.horn at aihw.gov.au Wed Jan 2 01:18:41 2002 From: graham.horn at aihw.gov.au (Horn, Graham) Date: Fri Oct 10 03:32:41 2003 Subject: KIF: "Abstract" and "dimensionality" - Re: SUMO axiomatization Message-ID: John et al, . I have had considerable problems with trying to tie down the nature of pure structure, theory, etc. I tried to apply the term "concept" to this, but was ruled out of order on the basis that a concept had to have been conceived by someone, and by implication, at a given point in time. The latest draft of ISO/IEC 11179?3 accordingly defines "Concept" as * "a unit of thought constituted through abstraction based on characteristics common to a set of objects". . I fear the same attitude may be taken to "Abstract", since someone had to perform the (mental) task of "drawing away" the pattern or structure from the original observation or thought. . Personally, I feel there is something in the nature of pure structure or pattern that can exist independently of whether it exists in physical reality, and also independently of whether any intelligent being has conceived of or observed it. . By way of explanation, I would suggest that both Newton's law of gravity and Kepler's laws of planetary motion are not precisely accurate, and so do not exist in physical reality, but are rather mere approximations of physical reality. Yet, I would suggest that they are both timeless and without location or mass ("zero?dimensional" in the physical sense), and hence existed infinitely before either Newton or Kepler were born, and will continue to do so after all records and other traces of them have been obliterated. . The problem is I don't know what term I can use to apply to such pure structures or patterns that one can abstract or conceive. . Neither does "information" cover this. One can observe and document the spread of information, whether be it physical, such as through the spread of genes, etc., or purely conceptual, such as with nemes, by means of, say, semaphore communication. . The reason I ask this question is that there are times when I wish to consider these "zero?dimensional" patterns / structures. . Incidentally, t have a related problem about the nature of "dimensionality". I wish to apply the term beyond the traditional physics scope of mass, length and time, into far more abstract areas. This is because it can be extremely useful in information management and information based sciences to apply to a far broader range of concepts. Statisticians psychologists and pharmacists do this when they are looking to ascertain which factors are relevant, and which irrelevant, for particular avenues of research and endeavour. The concept of "dimensionality", along with others like "mutual exclusivity" or "orthogonality" also come into play here, and can greatly facilitate conceptual design and analysis. . Can anyone suggest a rigorous definition that covers this broader scope? Cheers Graham Horn National Data Standards Unit Australian Institute of Health and Welfare ================================================ Phone: 02.6244.1094 Fax: 02.6244.1199 E?mail: Graham.Horn@aihw.gov.au Knowledgebase: www.aihw.gov.au/knowledgebase/ -----Original Message----- From: John F. Sowa [mailto:sowa@bestweb.net] Sent: Wednesday, 2 January 2002 14:28 To: kif@philebus.tamu.edu Cc: standard-upper-ontology@ieee.org Subject: SUO: Re: KIF: Re: SUMO axiomatization Chris, I would include all mathematical structures under the category Abstract in my ontology. In fact, everything under that category is of the same nature as Abstract; i.e., it is the category of every kind of form that can be defined without contradiction. The subtype Schema includes all the "static" structures, and the subtype Script includes all the "dynamic" structures -- i.e., all those that have a time-like succession of forms. As Nicola keeps insisting, the category of abstractions is outside of space & time. That is true, but you can have mathematical theories that include a dimension labeled t, which just happens to be very time-like. "Christopher A. Welty" wrote: CW> Thanks for pointing this out, John. It brings up an interesting > point for me - (sorry if this was discussed already during my > SUO-absence) - do people find this to be "upper level"? Certainly if > graphs is considered upper level, then this library demonstrates that > there are over a hundred other things at the same "level". At 1:55 PM -0500 12/22/01, John F. Sowa wrote: JFS>There is a collection of over a hundred mathematical theories > >(fully axiomatized) that were developed to run under IMPS > >(Interactive Mathematical Proof System). The theorem-proving > >programs that use these axioms run on most versions of LISP and > >are available from Mitre as software that has been made freely > >available. Following is the home page: > > > > http://imps.mcmaster.ca/ > > > >The theories include graphs, groups, fields, automata, > >and several versions of geometry, arithmetic, etc. The category of all abstractions has forms for everything that exists and everything that might exist without contradiction in any kind of universe. So it is even richer than the category Physical, which only includes those kinds of things that are physically possible in our universe. All those theories can be organized in a lattice, according to the partial ordering defined by implication; i.e., if every axiom of theory A is a theorem of theory B, then A is more general than B. But not all mathematical theories are in the upper level. Chess, for example, is a mathematical theory, but it would be farther down the hierarchy. And I would also include the mathematical forms of virtual reality under the category of abstractions. For examples, see the following web site, which has a couple of frames from a recent movie. It took 90 minutes of time on a supercomputer to do all the computations for each frame: http://a330.g.akamai.net/7/330/2540/e15dfb847b2b87/www.e-insite.net/ednmag/c ontents/images/185947f6.pdf All the computer is doing is generating lots of colored polygons. Those polygons would be fairly far down the hierarchy, but they're still abstract. John -------------- next part -------------- An HTML attachment was scrubbed... URL: http://philebus.tamu.edu/pipermail/kif/attachments/20020102/3be90f54/attachment.htm From ddiamond at ozemail.com.au Wed Jan 2 06:25:52 2002 From: ddiamond at ozemail.com.au (Chris Lofting) Date: Fri Oct 10 03:32:41 2003 Subject: KIF: RE: "Abstract" and "dimensionality" - Re: SUMO axiomatization In-Reply-To: Message-ID: "Abstract" and "dimensionality" - Re: SUMO axiomatization -----Original Message----- From: owner-standard-upper-ontology@majordomo.ieee.org [mailto:owner-standard-upper-ontology@majordomo.ieee.org]On Behalf Of Horn, Graham Sent: Wednesday, 2 January 2002 6:19 To: 'John F. Sowa'; kif@philebus.tamu.edu Cc: standard-upper-ontology@ieee.org Subject: SUO: "Abstract" and "dimensionality" - Re: SUMO axiomatization John et al, . I have had considerable problems with trying to tie down the nature of pure structure, theory, etc. I tried to apply the term "concept" to this, but was ruled out of order on the basis that a concept had to have been conceived by someone, and by implication, at a given point in time. The latest draft of ISO/IEC 11179?3 accordingly defines "Concept" as ? "a unit of thought constituted through abstraction based on characteristics common to a set of objects". . I fear the same attitude may be taken to "Abstract", since someone had to perform the (mental) task of "drawing away" the pattern or structure from the original observation or thought. . Personally, I feel there is something in the nature of pure structure or pattern that can exist independently of whether it exists in physical reality, and also independently of whether any intelligent being has conceived of or observed it. Since all of our maps/categories of reality seem to be based on self-referencing so a 'pure' structure or pattern is only reducable to the format we use at the mindless level. As such you can use the term 'Construct' since our self-referencing processes construct reality out of the 'mindless' , concrete level of sensory processing where intergration of data works to create a 'whole' that we then use self-reference to get the 'details' - this latter process reflects spectrum aquisition as we go for the parts-list. The realm of self-reference is VERY precise but also very archetypal, ideal forms etc and as such has a mechanistic perspective but then a parts list IS what is reflected in ontology. The 'fun' comes when the set of possible categories is introduced into reality - thus we link the static with the dynamic and from that elicit 'meanings' that are grounded to a context and so the sameness of the parts list serves to identify differences. Chris. -------------- Chris Lofting Websites: http://pages.prodigy.net/lofting http://www.ozemail.com.au/~ddiamond http://www.eisa.net.au/~lofting List owner: http://www.yahoogroups.com/group/semiosis http://www.yahoogroups.com/group/ichingplus -------------- next part -------------- An HTML attachment was scrubbed... URL: http://philebus.tamu.edu/pipermail/kif/attachments/20020102/b21dd0a3/attachment.htm From mpool at iet.com Wed Jan 2 12:10:44 2002 From: mpool at iet.com (Mike Pool) Date: Fri Oct 10 03:32:41 2003 Subject: KIF: Re: SUO: "Abstract" and "dimensionality" - Re: SUMO axiomatization In-Reply-To: Message-ID: <200201021806.NAA03581@central.iet.com> Dear Graham: See comment below. best, Mike Pool At 06:18 PM 02/01/02 +1100, Horn, Graham wrote: > > John et al, > ??????? .?????? ??????? I have had considerable problems with trying to tie > down the nature of pure structure, theory, etc. I tried to apply the term > "concept" to this, but was ruled out of order on the basis that a concept had > to have been conceived by someone, and by implication, at a given point in > time. The latest draft of ISO/IEC?11179?3 accordingly defines "Concept" as > > ??????? "a unit of thought constituted through abstraction based on > characteristics common to a set of objects". > > ??????? .?????? I fear the same attitude may be taken to "Abstract", since > someone had to perform the (mental) task of "drawing away" the pattern or > structure from the original observation or thought. Others have already made helpful responses but I thought I'd point out that there is a nice discussion of the notion of an "abstract object", and some of the difficulties in drawing a distinction between these and concrete objects, in the online Stanford Encyclopedia of Philosophy: http://plato.stanford.e du/entries/abstract-objects/ The phrase 'abstract object' is often used to denote much more than just the set of objects that have resulted from the mental process of abstraction, a distinction Frege tooks pains to elaborate. I wouldn't hesitate to use it to denote the entire set of (possibly mind-independent) non-concrete entities. As noted, the term is frustratingly vague but that doesn't mean that it's illegitimate or inaccurate to use it in the context(s) you describe. > > ??????? .?????? Personally, I feel there is something in the nature of pure > structure or pattern that can exist independently of whether it exists in > physical reality, and also independently of whether any intelligent being has > conceived of or observed it. > > ??????? .?????? By way of explanation, I would suggest that both Newton's law > of gravity and Kepler's laws of planetary motion are not precisely accurate, > and so do not exist in physical reality, but are rather mere approximations of > physical reality. Yet, I would suggest that they are both timeless and > without location or mass ("zero?dimensional" in the physical sense), and > hence existed infinitely before either Newton or Kepler were born, and will > continue to do so after all records and other traces of them have been > obliterated. > > ??????? .?????? The problem is I don't know what term I can use to apply to > such pure structures or patterns that one can abstract or conceive. > > ??????? .?????? Neither does "information" cover this. One can observe and > document the spread of information, whether be it physical, such as through > the spread of genes, etc., or purely conceptual, such as with nemes, by means > of, say, semaphore communication. > > ??????? .?????? The reason I ask this question is that there are times when I > wish to consider these "zero?dimensional" patterns /?structures. > > > ??????? .?????? Incidentally, t have a related problem about the nature of > "dimensionality". I wish to apply the term beyond the traditional physics > scope of mass, length and time, into far more abstract areas. This is because > it can be extremely useful in information management and information based > sciences to apply to a far broader range of concepts. Statisticians > psychologists and pharmacists do this when they are looking to ascertain > which factors are relevant, and which irrelevant, for particular avenues of > research and endeavour. The concept of "dimensionality", along with others > like "mutual exclusivity" or "orthogonality" also come into play here, and > can greatly facilitate conceptual design and analysis. > > ??????? .?????? Can anyone suggest a rigorous definition that covers this > broader scope? > > > Cheers?? ?????? ??????? ??????? ??????? Graham?Horn > National Data Standards Unit > Australian Institute of Health and Welfare? > ================================================ > Phone:????? ??? ??????? 02.6244.1094?? > Fax:????????? ? ??????? 02.6244.1199?? > E?mail:??? ???? ??????? > Graham.Horn@aihw.gov.au???? > Knowledgebase:? www.aihw.gov.au/knowledgebase/???? > > -----Original Message----- > From:?? John F. Sowa [mailto:sowa@bestweb.net] > Sent:?? Wednesday, 2 January 2002 14:28 > To:???? kif@philebus.tamu.edu > Cc:???? standard-upper-ontology@ieee.org > Subject:??????? SUO: Re: KIF: Re: SUMO axiomatization > > Chris, > > I would include all mathematical structures under the category Abstract > in my ontology.? In fact, everything under that category is of the > same nature as Abstract; i.e., it is the category of every kind of > form that can be defined without contradiction. > > The subtype Schema includes all the "static" structures, and the > subtype Script includes all the "dynamic" structures -- i.e., all > those that have a time-like succession of forms.? As Nicola keeps > insisting, the category of abstractions is outside of space & time. > That is true, but you can have mathematical theories that include > a dimension labeled t, which just happens to be very time-like. > > "Christopher A. Welty" wrote: > ? > CW> Thanks for pointing this out, John.? It brings up an interesting > > point for me - (sorry if this was discussed already during my > > SUO-absence) - do people find this to be "upper level"?? Certainly if > > graphs is considered upper level, then this library demonstrates that > > there are over a hundred other things at the same "level". > > At 1:55 PM -0500 12/22/01, John F. Sowa wrote: > > JFS>There is a collection of over a hundred mathematical theories > > >(fully axiomatized) that were developed to run under IMPS > > >(Interactive Mathematical Proof System).? The theorem-proving > > >programs that use these axioms run on most versions of LISP and > > >are available from Mitre as software that has been made freely > > >available.? Following is the home page: > > > > > >??? http://imps.mcmaster.ca/ > > > > > >The theories include graphs, groups, fields, automata, > > >and several versions of geometry, arithmetic, etc. > > The category of all abstractions has forms for everything that exists > and everything that might exist without contradiction in any kind of > universe.? So it is even richer than the category Physical, which only > includes those kinds of things that are physically possible in our > universe. > > All those theories can be organized in a lattice, according to > the partial ordering defined by implication; i.e., if every axiom > of theory A is a theorem of theory B, then A is more general than B. > > But not all mathematical theories are in the upper level.? Chess, > for example, is a mathematical theory, but it would be farther down > the hierarchy. > > And I would also include the mathematical forms of virtual reality > under the category of abstractions.? For examples, see the following > web site, which has a couple of frames from a recent movie.? It took > 90 minutes of time on a supercomputer to do all the computations for > each frame: > > ? > > > g/contents/images/185947f6.pdf>http://a330.g.akamai.net/7/330/2540/e15dfb8 > 47b2b87/www.e-insite.net/ednmag/contents/images/185947f6.pdf > > All the computer is doing is generating lots of colored polygons. > Those polygons would be fairly far down the hierarchy, but they're > still abstract. > > John ________________________________ Mike Pool Information Extraction & Transport, Inc. (703) 841-3500 x632 (703) 841-3501 Fax From sowa at bestweb.net Wed Jan 2 12:44:50 2002 From: sowa at bestweb.net (John F. Sowa) Date: Fri Oct 10 03:32:42 2003 Subject: KIF: Re: SUO: "Abstract" and "dimensionality" - Re: SUMOaxiomatization References: <200201021806.NAA03581@central.iet.com> Message-ID: <3C335522.F1D19E6D@bestweb.net> Mike et al., That article about abstract objects in the Stanford Encyclopedia is useful, but the author, like most 20th century analytic philosophers, is unfortunately ignorant of the history of his own subject. He cites Frege as the chief authority for the fundamental distinctions, even though Frege was almost as confused as his buddies. In the passage below, I have copied the excerpt from the Stanford Encyc. article that discusses Frege's contribution. I certainly agree that Frege was a very smart guy. But like most people who quote him, Frege was ignorant of the long history of logic, especially the major contributions by the medieval scholastics. Frege preached against "psychologism" in logic, but he constantly fell back into the old muddled ways of thought in his own terminology, with his repeated use of words like "Gedanke" (thought) and "Urteil" (judgment). Peirce used the scholastic term "propositio" (proposition), which is sufficiently neutral to serve as the "mind-independent" content without presupposing a necessary dependence on any kind of mind. Even though the scholastics were devoted Christians (and one of the chief authors, Peter of Spain, later became Pope John XXI), they were never so naive as to claim support from the "mind of God" in order to develop logic. Most of the following quotation discusses ways out of Frege's muddle, which the medieval scholastics and, of course, Peirce avoided with their more sophisicated theories of semiotics. The author also mentions Bolzano and Brentano as having made claims that were "similar" to Frege's. That also distorts history, since both of them were very familiar with the scholastic writings, and unlike Frege, they did not succumb to the muddled terminology that they were arguing against. John Sowa _____________________________________________________________________ Source: http://plato.stanford.edu/entries/abstract-objects/ One signal event in this development is Frege?s insistence that the objectivity and a priori of the truths of mathematics entail that numbers are neither material beings nor ideas in the mind. If numbers were material things (or properties of material things), the laws of arithmetic would have the status of empirical generalizations. If numbers were ideas in the mind, then the same difficulty would arise, as would countless others. (Whose mind contains the number 17? Is there one 17 in your mind and another in mine? In that case, the appearance of a common mathematical subject matter is an illusion.) In The Foundations of Arithmetic (1884), Frege concludes that numbers are neither external ?concrete? things nor mental entities of any sort. Later, in his essay "The Thought" (Frege 1918), he claims the same status for the items he calls thoughts -- the senses of declarative sentences -- and also, by implication, for their constituents, the senses of subsentential expressions. Frege does not say that senses are "abstract". He says that they belong to a "third realm" distinct both from the sensible external world and from the internal world of consciousness. Similar claims had been made by Bolzano (1837), and later by Brentano (1874) and his pupils, including Meinong and Husserl. The common theme in these developments is the felt need in semantics and psychology as well as in mathematics for a class of objective (i.e., non-mental) supersensible entities. As this new "realism" was absorbed into English speaking philosophy, the traditional term "abstract" was enlisted to apply to the denizens of this "third realm". Frege?s way of drawing the distinction is an instance of what Lewis (1986) calls the Way of Negation. Abstract objects are defined as those that lack certain features possessed by paradigmatic concrete things. Nearly every explicit characterization in the literature has this feature. There are, however, several significant difficulties with this approach, at least in its most familiar implementations. According to Frege?s explicit account, the items in the "third realm" are non-mental and non-sensible. But it is unclear what it means to call an object mental or mind-dependent; and to the extent that the notion is intelligible, it is quite unclear whether abstract objects in general satisfy the condition. It is commonly supposed, for example, that the game of chess is an abstract entity (Dummett 1973). But there is certainly a sense in which the game would not have existed were it not for the mental activity of human beings. So at least one sort of mind-dependence would appear to be compatible with abstractness. Moreover, it has sometimes been maintained that the paradigmatic abstract entities -- mathematical objects, universals -- exist only as ideas in the mind of God. The view may be outlandish; but is it a view according to which abstract entities do not exist? Or is it rather a view ccording to which certain abstract entities are also mind-dependent? Insofar as the latter interpretation is not straightforwardly contradictory, the definition of "abstract" should not require mind-independence. Perhaps more importantly, Frege?s identification of the abstract with the realm of non-sensible non-mental things entails that unobservable physical objects such as quarks and electrons should be classified as abstract entities. But this is at odds with standard usage, and almost certainly with Frege?s intention. From cmenzel at tamu.edu Fri Jan 18 21:50:52 2002 From: cmenzel at tamu.edu (Chris Menzel) Date: Fri Oct 10 03:32:42 2003 Subject: [KIF] New mailing list Message-ID: <20020119035052.GK7297@tamu.edu> Folks, As you will probably have surmised from the welcome msg you received, I have moved our KIF mailing list from majordomo to Mailman, a far more competent list management program. It lets you manage your own subscription very conveniently via the web. (See the URLs in the welcome msg.) It also uses pipermail to manage the list archive. Pipermail breaks down into monthly installments, which in turn can be sorted by thread, subject, author, or date. I have converted all of our old KIF archives to the pipermail format, so it will be as if we've used Mailman all along. Let me know if you have any questions or problems. -chris From cmenzel at tamu.edu Fri Jan 18 22:58:24 2002 From: cmenzel at tamu.edu (Chris Menzel) Date: Fri Oct 10 03:32:42 2003 Subject: [KIF] New list software Message-ID: <20020119045824.GL7297@tamu.edu> Folks, As you will probably have surmised from the welcome msg you received, I have moved our KIF mailing list from majordomo to Mailman, a far more competent list management program. It lets you manage your own subscription very conveniently via the web. (See the URLs in the welcome msg.) It also uses pipermail to manage the list archive. Pipermail breaks down into monthly installments, which in turn can be sorted by thread, subject, author, or date. I have converted all of our old KIF archives to the pipermail format, so it will be as if we've used Mailman all along. Let me know if you have any questions or problems. -chris From phayes at ai.uwf.edu Tue Jan 22 14:21:29 2002 From: phayes at ai.uwf.edu (Pat Hayes) Date: Fri Oct 10 03:32:42 2003 Subject: [KIF] Re: KIF: Re: SUO: RE: SUMO axiomatization In-Reply-To: <5.1.0.14.2.20011220120504.0200b1f0@ks.teknowledge.com> References: <5.1.0.14.2.20011220120504.0200b1f0@ks.teknowledge.com> Message-ID: >Chris, > Ok, maybe I've got it wrong - can you provide an example of a >definition that is useful in the context of SUMO, and which is >possible with row variables, but not without? (Sorry this response is delayed, but...) Let me interject with some examples. 1. The definition of lists. 2. The possibility of defining finiteness of abstract structures. 3. The ability to state that a recursive definition is restricted to finite cases. 4. The ability to define general second-order relational properties such as those of 'predicative' and 'chained' used in my 'time catalog': ;;predicative-BASIC (defrelation predicative (?r) := (forall (?x @l) (<=> (?r ?x @l) (and (?r ?x) (?r @l))))) ;;chained-BASIC (defrelation chained (?r) := (forall (?x ?y @l) (<=> (?r ?x ?y @l) (and (?r ?x ?y) (?r ?y @l))))) ;;BASIC-syntax (predicative predicative chained) BTW, to address your point in these messages that some of the divergences of opinion are simply matters of taste or aesthetics; I would agree, but would add that in such a case, since there is no obligation on anyone to use a feature that they find ugly, whereas omitting it from the language makes it impossible for anyone else to use it, that it is clear that in such cases of divergence of opinion, the only reasonable way to proceed is to include the feature in the language as an option. Pat >Adam > >At 01:57 PM 12/20/2001 -0600, Chris Menzel wrote: >>Adam wrote: >>> The point about language complexity is not really debatable. I think it >>> makes the syntax more complex which I consider simply equivalent to a >>> factual statement that it requires more clauses in the BNF grammar. You >>> could interpret "more complex" differently. You could say (as Bill and >>> Chris have) that "more complex" refers to the axioms that are needed to >>> define particular concepts in the ontology. They've shown good examples of >>> how row variables make for more compact definitions. >> >>That doesn't put the point strongly enough, Adam. Row variables don't >>simply make for more compact definitions. More typically, they make >>certain *possible* that are impossible without them. They wouldn't be >>terribly interesting if they simply saved a few bytes. Row variables make >>KIF strictly more expressive than first-order. >> >>> Are they simpler or easier to understand? It depends on what community >>> you're addressing, and comes down to personal preference, not a statement >>> of right or wrong. >> >>That would be so only if the added mechanisms (as in the case of sorts) >>added no expressive power -- and even then it might not be a matter of >>preference, as certain constructs might make for better computational >>efficiency. Either way, it seems to me the issue isn't personal >>preference, but rather whether the constructs in question are useful for >>building and/or reasoning upon ontologies. >> >>-chris >> >>-- >> >> /\ ASCII ribbon | Chris Menzel -- http://philebus.tamu.edu/~cmenzel >> \/ campaign | Philosophy Dept, Texas A&M University >> /\ against | College Station, TX 77843-4237 >>/ \ HTML email | voice: 979.845-5660 fax: 979.845.0458 > >Adam Pease >Teknowledge >(650) 424-0500 x571 -- --------------------------------------------------------------------- IHMC (850)434 8903 home 40 South Alcaniz St. (850)202 4416 office Pensacola, FL 32501 (850)202 4440 fax phayes@ai.uwf.edu http://www.coginst.uwf.edu/~phayes From apease at ks.teknowledge.com Tue Jan 22 14:32:01 2002 From: apease at ks.teknowledge.com (Adam Pease) Date: Fri Oct 10 03:32:43 2003 Subject: [KIF] Re: KIF: Re: SUO: RE: SUMO axiomatization In-Reply-To: References: <5.1.0.14.2.20011220120504.0200b1f0@ks.teknowledge.com> <5.1.0.14.2.20011220120504.0200b1f0@ks.teknowledge.com> Message-ID: <5.1.0.14.2.20020122122927.02c0b008@ks.teknowledge.com> Pat, Hey, we already agreed to use row variables, no more convincing is necessary :-) I don't agree with your general point that we should include all the features anyone likes. That would result in a bloated product, roughly analogous to the earliest versions of KIF or say, common LISP, that would be very difficult to implement. Adam At 02:21 PM 1/22/2002 -0600, Pat Hayes wrote: >>Chris, >> Ok, maybe I've got it wrong - can you provide an example of a >> definition that is useful in the context of SUMO, and which is possible >> with row variables, but not without? > >(Sorry this response is delayed, but...) Let me interject with some examples. > >1. The definition of lists. >2. The possibility of defining finiteness of abstract structures. >3. The ability to state that a recursive definition is restricted to >finite cases. >4. The ability to define general second-order relational properties such >as those of 'predicative' and 'chained' used in my 'time catalog': >;;predicative-BASIC >(defrelation predicative (?r) := > (forall (?x @l) > (<=> > (?r ?x @l) > (and (?r ?x) (?r @l))))) > >;;chained-BASIC >(defrelation chained (?r) := > (forall (?x ?y @l) (<=> (?r ?x ?y @l) > (and (?r ?x ?y) (?r ?y @l))))) > >;;BASIC-syntax >(predicative predicative chained) > >BTW, to address your point in these messages that some of the divergences >of opinion are simply matters of taste or aesthetics; I would agree, but >would add that in such a case, since there is no obligation on anyone to >use a feature that they find ugly, whereas omitting it from the language >makes it impossible for anyone else to use it, that it is clear that in >such cases of divergence of opinion, the only reasonable way to proceed is >to include the feature in the language as an option. > >Pat > > >>Adam >> >>At 01:57 PM 12/20/2001 -0600, Chris Menzel wrote: >>>Adam wrote: >>>> The point about language complexity is not really debatable. I think it >>>> makes the syntax more complex which I consider simply equivalent to a >>>> factual statement that it requires more clauses in the BNF grammar. You >>>> could interpret "more complex" differently. You could say (as Bill and >>>> Chris have) that "more complex" refers to the axioms that are needed to >>>> define particular concepts in the ontology. They've shown good >>>> examples of >>>> how row variables make for more compact definitions. >>> >>>That doesn't put the point strongly enough, Adam. Row variables don't >>>simply make for more compact definitions. More typically, they make >>>certain *possible* that are impossible without them. They wouldn't be >>>terribly interesting if they simply saved a few bytes. Row variables make >>>KIF strictly more expressive than first-order. >>> >>>> Are they simpler or easier to understand? It depends on what community >>>> you're addressing, and comes down to personal preference, not a statement >>>> of right or wrong. >>> >>>That would be so only if the added mechanisms (as in the case of sorts) >>>added no expressive power -- and even then it might not be a matter of >>>preference, as certain constructs might make for better computational >>>efficiency. Either way, it seems to me the issue isn't personal >>>preference, but rather whether the constructs in question are useful for >>>building and/or reasoning upon ontologies. >>> >>>-chris >>> >>>-- >>> >>> /\ ASCII ribbon | Chris Menzel -- http://philebus.tamu.edu/~cmenzel >>> \/ campaign | Philosophy Dept, Texas A&M University >>> /\ against | College Station, TX 77843-4237 >>>/ \ HTML email | voice: 979.845-5660 fax: 979.845.0458 >> >>Adam Pease >>Teknowledge >>(650) 424-0500 x571 > > >-- >--------------------------------------------------------------------- >IHMC (850)434 8903 home >40 South Alcaniz St. (850)202 4416 office >Pensacola, FL 32501 (850)202 4440 fax >phayes@ai.uwf.edu http://www.coginst.uwf.edu/~phayes > >_______________________________________________ >KIF mailing list >KIF@philebus.tamu.edu >http://philebus.tamu.edu/mailman/listinfo/kif Adam Pease Teknowledge (650) 424-0500 x571 From andersen at ontologyworks.com Tue Jan 22 14:49:57 2002 From: andersen at ontologyworks.com (Bill Andersen) Date: Fri Oct 10 03:32:43 2003 Subject: [KIF] Re: KIF: Re: SUO: RE: SUMO axiomatization In-Reply-To: <5.1.0.14.2.20020122122927.02c0b008@ks.teknowledge.com> Message-ID: On 1/22/02 14:32, "Adam Pease" wrote: > Pat, > Hey, we already agreed to use row variables, no more convincing is > necessary :-) > > I don't agree with your general point that we should include all the > features anyone likes. That would result in a bloated product, roughly > analogous to the earliest versions of KIF or say, common LISP, that would > be very difficult to implement. > > Adam > > At 02:21 PM 1/22/2002 -0600, Pat Hayes wrote: >>> Chris, >>> Ok, maybe I've got it wrong - can you provide an example of a >>> definition that is useful in the context of SUMO, and which is possible >>> with row variables, but not without? >> >> (Sorry this response is delayed, but...) Let me interject with some examples. >> >> 1. The definition of lists. >> 2. The possibility of defining finiteness of abstract structures. >> 3. The ability to state that a recursive definition is restricted to >> finite cases. >> 4. The ability to define general second-order relational properties such >> as those of 'predicative' and 'chained' used in my 'time catalog': >> ;;predicative-BASIC >> (defrelation predicative (?r) := >> (forall (?x @l) >> (<=> >> (?r ?x @l) >> (and (?r ?x) (?r @l))))) >> >> ;;chained-BASIC >> (defrelation chained (?r) := >> (forall (?x ?y @l) (<=> (?r ?x ?y @l) >> (and (?r ?x ?y) (?r ?y @l))))) >> >> ;;BASIC-syntax >> (predicative predicative chained) Pat, These definitions look interesting, but I'm not sure I understand what they're intended to do. Could you expand a bit? Yep - I also spent a lot of time explaining examples to Ian using row and predicate/function variables, so they're on board now. .bill From phayes at ai.uwf.edu Tue Jan 22 19:39:35 2002 From: phayes at ai.uwf.edu (Pat Hayes) Date: Fri Oct 10 03:32:44 2003 Subject: [KIF] Re: KIF: Re: SUO: RE: SUMO axiomatization In-Reply-To: References: Message-ID: > >> 4. The ability to define general second-order relational properties such >>> as those of 'predicative' and 'chained' used in my 'time catalog': >>> ;;predicative-BASIC >>> (defrelation predicative (?r) := >>> (forall (?x @l) >>> (<=> >>> (?r ?x @l) >>> (and (?r ?x) (?r @l))))) >>> >>> ;;chained-BASIC >>> (defrelation chained (?r) := >>> (forall (?x ?y @l) (<=> (?r ?x ?y @l) >>> (and (?r ?x ?y) (?r ?y @l))))) >>> >>> ;;BASIC-syntax >>> (predicative predicative chained) > >Pat, > >These definitions look interesting, but I'm not sure I understand what >they're intended to do. Could you expand a bit? Sure. Predicative says that its argument is a relation which when applied to a number of arguments is equivalent to being applied (as a predicate) to each of them in turn, which is a handy way to encode conjunctions. Chained says that its argument is a relation which when applied to a number of arguments is equivalent to being applied as a binary relation to each pair in the sequence, which allows you to write things like (and (integer a b c d e)(less-than a b c d e)) to indicate a well-ordered series, if you have asserted (predicative integer) and (chained less-than). The real utility is being able to write (and (integer @x)(less-than @x)) , of course, to quantify over *all* well-ordered series of integers. I found these very handy in axiomatizing relationships between calendars and clocks, and more generally for stating all kinds of relationships between linear series in terms of those on their members. (They obviously generalize, and one could even state the generalized axiom using integers, but I never seemed to need anything past the binary case.) > >Yep - I also spent a lot of time explaining examples to Ian using row and >predicate/function variables, so they're on board now. Yes, I saw that after sending the above. Pat -- --------------------------------------------------------------------- IHMC (850)434 8903 home 40 South Alcaniz St. (850)202 4416 office Pensacola, FL 32501 (850)202 4440 fax phayes@ai.uwf.edu http://www.coginst.uwf.edu/~phayes From phayes at ai.uwf.edu Tue Jan 22 20:00:43 2002 From: phayes at ai.uwf.edu (Pat Hayes) Date: Fri Oct 10 03:32:44 2003 Subject: [KIF] Re: KIF: Re: SUO: RE: SUMO axiomatization In-Reply-To: <5.1.0.14.2.20020122122927.02c0b008@ks.teknowledge.com> References: <5.1.0.14.2.20011220120504.0200b1f0@ks.teknowledge.com> <5.1.0.14.2.20011220120504.0200b1f0@ks.teknowledge.com> <5.1.0.14.2.20020122122927.02c0b008@ks.teknowledge.com> Message-ID: >Pat, > Hey, we already agreed to use row variables, no more convincing is >necessary :-) Yes, sorry i hadnt read that when i sent the message. Im catching up on about 400 emails and SUO is rather delayed. > I don't agree with your general point that we should include all >the features anyone likes. That would result in a bloated product, >roughly analogous to the earliest versions of KIF or say, common >LISP, that would be very difficult to implement. I don't want to include all the features that anyone likes, only a basic suite of features that quite a lot of people like. And I profoundly disagree with your reasoning. First, its a standard, not a product; second, there is no obligation on anyone to implement all of it; third, in any case, I disagee that it would be all that hard to implement many useful parts even of the fullest spec that we have ever considered, eg a parser, editors, search tools, etc. (A complete inference engine is something else again.) Fourthly, you have applied this criterion even to elementary features of general utility, such as allowing empty conjunctions, or the use of syntactic typing, or web-savvy ontology importing/reference tools. But the main thing is that by including features we *allow* them to be used, and by deleting them we *forbid* them to be used, and the distinction is crucial. BUt lets not have this quarrel again. I plan to utilize a different pathway to a reasonable standard in any case. Pat -- --------------------------------------------------------------------- IHMC (850)434 8903 home 40 South Alcaniz St. (850)202 4416 office Pensacola, FL 32501 (850)202 4440 fax phayes@ai.uwf.edu http://www.coginst.uwf.edu/~phayes From weltyc at cs.vassar.edu Fri Jan 25 18:23:44 2002 From: weltyc at cs.vassar.edu (Christopher A. Welty) Date: Fri Oct 10 03:32:44 2003 Subject: [KIF] Levels of conformance In-Reply-To: References: <5.1.0.14.2.20011220120504.0200b1f0@ks.teknowledge.com> <5.1.0.14.2.20011220120504.0200b1f0@ks.teknowledge.com> <5.1.0.14.2.20020122122927.02c0b008@ks.teknowledge.com> Message-ID: Mike G. and I spent a few days together at NIST this week, and discussed among other things the KIF standardization effort. It has been over a year and a half since we began this discussion, and over a year has passed since College Station. One of the most controversial points that has recurred in our discussions in this group has been the idea of a small "KIF Core", its relationship to things like "sorts" and other notions that we decided at some point to call "extensions", and how to express this in the KIF spec in general. It was never clear to what degree this group agreed on what should be in the "core", what were extensions to the core, etc. As this group became more aware of what would be required of KIF as a standard, we also began to discover that "levels of conformance" would be something we should specify, and this was introduced into the mix as an additional - though possibly overlapping - issue. Mike and I talked about this and about the fact that we were having so much trouble achieving consensus, and remembering it when we did. I was one of the ones who has been repeatedly insisting on a small KIF-core, and relegating things like sorts, an "include" directive, namespaces, etc., to extensions. Mike was, rather, in favor of having just one spec with two levels of "semantic" conformance corresponding to first-order and infinitary model theories. We then began to pick at each other's arguments and realized that, for both of us, the distinctions for what made an "extension" or a "level of semantic conformance" were actually quite arbitrary. We were each able to come up with examples of systems - existing systems - that would not correspond neatly to any combination of core+extensions nor either of the levels of semantic conformance. After some further discussion, we hit upon an idea that we both liked very much, as it seems to address both our concerns and provide simple ways for existing and new systems to precisely express their levels of conformance with KIF. This is, roughly, the proposal: 1. There will be two specs, *one* for the "Full" KIF (with sorts, namespaces, and anything else people want), and one for Meta-KIF. 2. Each system defines syntactic conformance by providing in Meta-KIF the (subset of the) KIF syntax it supports. 3. Each system defines semantic conformance in terms of Soundness, completeness, and decidability. This allows someone to define, in a sense, which parts of KIF they find "core" and which they do not. This would differ drastically, e.g., between the Prolog guys and the description logic guys. Adam can define his trimmed down unsorted KIF with no namespaces, and Mark can define a version that only supports row variables in the tail. I realize that something like this had already been suggested much earlier, but I, at least, never really put it together before. Sometimes it takes me a little while. -- Christopher A. Welty http://www.cs.vassar.edu/faculty/welty/ Vassar College Computer Science Dept. Voice: (845) 437-5992 Poughkeepsie, NY 12604-0462 Fax: (845) 437-7498 From sowa at bestweb.net Sat Jan 26 12:51:48 2002 From: sowa at bestweb.net (John F. Sowa) Date: Fri Oct 10 03:32:44 2003 Subject: [KIF] Levels of conformance References: <5.1.0.14.2.20011220120504.0200b1f0@ks.teknowledge.com> <5.1.0.14.2.20011220120504.0200b1f0@ks.teknowledge.com> <5.1.0.14.2.20020122122927.02c0b008@ks.teknowledge.com> Message-ID: <3C52FAC4.2FA3E9B4@bestweb.net> Chris, With some tinkering, I think that something along those lines could be defined: > 1. There will be two specs, *one* for the "Full" KIF (with sorts, > namespaces, and anything else people want), and one for Meta-KIF. > 2. Each system defines syntactic conformance by providing in Meta-KIF > the (subset of the) KIF syntax it supports. > 3. Each system defines semantic conformance in terms of Soundness, > completeness, and decidability. But we clearly have not been able to document our positions well enough for ourselves. If we have no idea what is in or out of the proposed standard, the rest of the world is completely in the dark. At the ISO WG32 meeting in October, our proposed New Work Item for the Logical Foundations was "well received", but the committee did not vote to accept it. Dan Gilman said that they were concerned that there was not enough support to maintain such a standard, even if we did finish it. And the absence of anyone (such as Mike or me) who could present or defend it was taken as evidence that there wasn't enough support for it. The next SG32 meeting is supposed to be in Korea in May. I will not be able to go there. Will Mike be able to go? It is very important that someone on this list be there to promote it. It is also very important for us to have another meeting before May in order to itemize exactly what we have decided (or to make those decisions and write them down). I suggest that Palo Alto around the end of March (before or during the AAAI Spring Syposium) would be a good time and place for such a meeting. John Sowa