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## Re: [ontolog-forum] Ontology, Information Models and the 'Real World': C

 To: "[ontolog-forum]" Waclaw Kusnierczyk Mon, 28 May 2007 18:57:46 +0200 <465B0A0A.1040604@xxxxxxxxxxx>
 ```John,    (01) That's a very useful summary. I do not think there were any doubt how the usual definition of 'asymmetric' goes. I had some doubt as to whether Pat has adopted another definition, but this issue has been succesfully solved.    (02) Thanks anyway.    (03) vQ    (04) John F. Sowa wrote: > Folks, > > I have a web page that gives a brief review and summary > of some basic topics and definitions in math and logic: > > http://www.jfsowa.com/logic/math.htm > Mathematical Background > > Following is the table of contents (each section takes about > 3 or 4 pages, if printed out). After that is an excerpt from > Section 5 on relations. > > John Sowa > _____________________________________________________________ > > 1. Sets, Bags, and Sequences > 2. Functions > 3. Lambda Calculus > 4. Graphs > 5. Relations > 6. Representing Relations by Graphs > 7. Lattices > 8. Propositional Logic > 9. Predicate Logic > 10. Axioms and Proofs > 11. Formal Grammars > 12. Game Graphs > 13. Model Theory > 14. References > > An excerpt from Section 5: > > The following table lists some common types of relations, an axiom that > states the defining constraint for each type, and an example of the > type. The symbol ® represents an arbitrary dyadic relation. > > Type Axiom Example > ---- ----- ------- > Reflexive (Ax)x®x x is as old as y > Irreflexive (Ax)not(x®x) x is the mother of y > Symmetric (Ax,y)(x®y -> y®x) x is the spouse of y > Asymmetric (Ax,y)(x®y -> not y®x) x is the husband of y > Antisymmetric (Ax,y)(x®y & y®x -> x=y) x was present at y's birth > Transitive (Ax,y)(x®y & y®z -> x®z) x is an ancestor of y > > The symbol A, called the universal quantifier, may be read "for every" > or "for all". It is discussed further in Section 9 on predicate logic. > Some important types of relations -- such as partial order, linear > order, and equivalence -- satisfy two or more of the above axioms: > > > _________________________________________________________________ > Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ > Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ > Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx > Shared Files: http://ontolog.cim3.net/file/ > Community Wiki: http://ontolog.cim3.net/wiki/ > To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx >    (05) -- Wacek Kusnierczyk    (06) ------------------------------------------------------ Department of Information and Computer Science (IDI) Norwegian University of Science and Technology (NTNU) Sem Saelandsv. 7-9 7027 Trondheim Norway    (07) tel. 0047 73591875 fax 0047 73594466 ------------------------------------------------------    (08) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (09) ```
 Current Thread Re: [ontolog-forum] Ontology, Information Models and the 'Real World': Contexts, KCliffer Re: [ontolog-forum] Ontology, Information Models and the 'Real World': Contexts, Waclaw Kusnierczyk Re: [ontolog-forum] Ontology, Information Models and the 'Real World': Contexts, John F. Sowa Re: [ontolog-forum] Ontology, Information Models and the 'Real World': Contexts, Duane Nickull Re: [ontolog-forum] Ontology, Information Models and the 'Real World': Contexts, John F. Sowa Re: [ontolog-forum] Ontology, Information Models and the 'Real World': Contexts, Waclaw Kusnierczyk Re: [ontolog-forum] Ontology, Information Models and the 'Real World': Contexts, Waclaw Kusnierczyk <= Re: [ontolog-forum] Ontology, Information Models and the 'Real World': Contexts, Christopher Menzel Re: [ontolog-forum] Ontology, Information Models and the 'Real World': Contexts, John F. Sowa Re: [ontolog-forum] Ontology, Information Models and the 'Real World': Contexts, Waclaw Kusnierczyk Re: [ontolog-forum] Ontology, Information Models and the 'Real World': Contexts, Pat Hayes