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From: epstein@sunc4.cs.uiuc.edu (Milt Epstein)
Newsgroups: comp.ai
Subject: Re: What is "fuzzy logic"?
Message-ID: <27F41DFC.3E0E@ibma0.cs.uiuc.edu>
Date: 30 Mar 91 05:11:24 GMT
References: <1991Mar28.192533.3272@waikato.ac.nz> <13842@ccncsu.ColoState.EDU> <1991Mar30.030729.15540@mercury.cair.du.edu>
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In <1991Mar30.030729.15540@mercury.cair.du.edu> ttoupin@diana.cair.du.edu (Tory Toupin) writes:

>While we are on the subject, what is the significance of the term "first order
>predicate calculus"?  What is "nth other predicate calculus"?  Perchance
>"fuzzy-logic"?

First-order means you can only quantify over objects in the domain of
discourse -- that is, variables can only represent objects.  In
second-order, you can quantify over functions and predicates, such as:

     (forall (P) (P A) ==> (P B))

(everything that is true of A is true of B).

I guess I had never dealt with anything beyond second-order, but I
found something about higher-order logics in "The Computer Modelling
Of Mathematical Reasoning" by Alan Bundy.  It talks about the ideas of
"functionals", "lambda abstractions" and "omega order logic", which I
have not really heard of before (except lambda abstractions).

Fuzzy logic, as some other people have pointed out, is something of a
cross between classical (two-valued) logic and probability (where you
have continuous values between 0 and 1).

-- 
Milt Epstein
Department of Computer Science
University of Illinois
epstein@cs.uiuc.edu