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

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Duane Nickull <dnickull@xxxxxxxxx>
Date: Mon, 28 May 2007 09:14:12 -0700
Message-id: <C2804DE4.F4DF%dnickull@xxxxxxxxx>
John:    (01)

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.    (02)

Duane    (03)


On 5/28/07 8:28 AM, "John F. Sowa" <sowa@xxxxxxxxxxx> wrote:    (04)

> 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)xx                    x is as old as y
>    Irreflexive  (Ax)not(xx)               x is the mother of y
>    Symmetric  (Ax,y)(xy -> yx)         x is the spouse of y
>    Asymmetric  (Ax,y)(xy -> not yx)     x is the husband of y
>    Antisymmetric (Ax,y)(xy & yx -> x=y)   x was present at y's birth
>    Transitive    (Ax,y)(xy & yz -> xz)   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:
> 
>  
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>      (05)


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