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

 To: "[ontolog-forum]" Waclaw Kusnierczyk Mon, 28 May 2007 19:00:56 +0200 <465B0AC8.2080104@xxxxxxxxxxx>
 ```On such occasions I also find useful "Mathematical Foundations of Computational Engineering: A Handbook" by Peter J. Pahl and Rudolf Damrath.    (01) http://tinyurl.com/2unao9    (02) vQ    (03) Duane Nickull wrote: > John: > > Many thanks. This is a great resource. Would you mind if I borrowed some > content for a presentation I am giving? I'll credit you as the source for > sure. > > Duane > > > On 5/28/07 8:28 AM, "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 >> > > > _________________________________________________________________ > 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 >    (04) -- Wacek Kusnierczyk    (05) ------------------------------------------------------ Department of Information and Computer Science (IDI) Norwegian University of Science and Technology (NTNU) Sem Saelandsv. 7-9 7027 Trondheim Norway    (06) tel. 0047 73591875 fax 0047 73594466 ------------------------------------------------------    (07) _________________________________________________________________ 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    (08) ```
 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