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Topic: [HM] Non-mathematical use of axiomatics
Replies: 14   Last Post: Dec 20, 2000 9:35 PM

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Antreas P. Hatzipolakis

Posts: 940
Registered: 12/3/04
Re: [HM] Non-mathematical use of axiomatics
Posted: Oct 24, 2000 3:46 PM
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A modern example: Noam Chomsky's axiomatization of Linguistics
[to recall another ongoing discussion in this list:
Where are you, Mr McCarthy, to "see" him?]

The basic system of description that we shall consider is a system G of
the following form: G is a semi-group under concatenation [see below] with
strings in a finite set V of symbols as its elements, and I as the identity
element. V is called the "vocabulary" of G. V = V_T U V_N (V_T, V_N
disjoint), where V_T is the "terminal vocabulary" and V_N the "nonterminal
vocabulary." A two-place relation -> is defined on elements of G, read
"can be rewritten as." This relation satisfies the following conditions:

AXIOM 1. -> is irreflexive.

[AXIOMs 2-4 omitted, due to symbols not available in the ASCII table]

Information and Control, 2,1959, p. 141.

I recall that I have read in a Greek book on the Middle Ages Philosophy
that some Catholic Theologians had tried to axiomatize Theology.
Details when I locate the book.


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