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

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Waclaw Kusnierczyk <Waclaw.Marcin.Kusnierczyk@xxxxxxxxxxx>
Date: Mon, 28 May 2007 19:00:56 +0200
Message-id: <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" <sowa@xxxxxxxxxxx> 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)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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> 
>  
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>      (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)

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