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)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)
|