From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1787 Path: news.gmane.org!not-for-mail From: mjhealy@redwood.rt.cs.boeing.com (Michael J. Healy 425-865-3123) Newsgroups: gmane.science.mathematics.categories Subject: Question Date: Tue, 16 Jan 2001 16:17:19 -0800 (PST) Message-ID: <200101170017.QAA12492@lilith.rt.cs.boeing.com> NNTP-Posting-Host: main.gmane.org X-Trace: ger.gmane.org 1241018102 461 80.91.229.2 (29 Apr 2009 15:15:02 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:15:02 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Tue Jan 16 21:06:15 2001 -0400 Return-Path: Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f0H0Q4l28728 for categories-list; Tue, 16 Jan 2001 20:26:04 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Sun-Charset: US-ASCII Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 18 Original-Lines: 78 Xref: news.gmane.org gmane.science.mathematics.categories:1787 Archived-At: I'd like to ask category theorists how they would answer the attached message from a colleague here. Both he and the person with whom he is corresponding are experts in the areas of knowledge representation within computer science (ontologies and the like). I thought it best to hide their identities since I haven't asked permission to use them. If you are interested, please respond to me privately if you would. Thank you, Mike Healy ------------------------------------------------------------------------------ Message I received:---- I would be delighted if there was no semantic conflict between category theory and set theory. I kind of flagged this as a potential issue, but did not look into it in detail, as it was not my main concern at the time. However, I remain unconvinced. There has been some discussion of using set theory as the basis for a semantics for SUOKIF. If this is true, then I think it may be limiting to a CT based language. While it may be true that sets are common example of a catagory, my sense is that CT is much more powerful, and would be LIMITED if everything was forced into the single catagory of sets. Im a bit out of my element here, however, and need to defer to the formal expertise of others on this issue. Message to which the above was replying:--- I agree that category theory is very powerful and could be an important basis for combining and sharing ontologies. But I disagree with the following point: >I think this idea has tremendous potential. One problem is that the underlying >formal semantics of category theory is NOT set theory (which is what KIF uses), >furthermore, I think they may well be incompatible. First-order logic (including any and all notations for it, such as KIF, CGs, predicate calculus, existential graphs, etc.) is completely neutral with respect to set theory or category theory. The version 3.0 of KIF did include a version of set theory, but that was removed in the KIF'99 version because it belongs to ontology rather than logic. And for that matter, there is no reason why you can't use both category theory and set theory together. In fact, one of the most common examples of a category is the category of sets. Perhaps there may be incompatibilities between the methodology associated with Ontolingua and category-based techiques, but Ontolingua is not KIF. Ontolingua simply uses KIF. -- =========================================================================== e Michael J. Healy A FA ----------> GA (425)865-3123 | | FAX(425)865-2964 | | Ff | | Gf c/o The Boeing Company | | PO Box 3707 MS 7L-66 \|/ \|/ Seattle, WA 98124-2207 ' ' USA FB ----------> GB -or for priority mail- e "I'm a natural man." 2760 160th Ave SE MS 7L-66 B Bellevue, WA 98008 USA michael.j.healy@boeing.com -or- mjhealy@u.washington.edu ============================================================================