# Fuzzy inference and logical consequence

hvirtane@kasper.abo.fi
Tue, 30 Apr 1996 15:17:29 +0200

Hi!

How would you people define logical consequence in approximated reasoning??

Compare with the classical case:
===================================
Modus ponens state that from A and A->B, we can infer B',
such that B'=B(S), where S is a substitution of variables.

Let A and A->B be the set of formulas P. Then we define
LOGICAL CONSEQUENCE as follows: B is a logical consequence
of P if and only if B is true in every model M of P.

And the Fuzzy case:
====================================
Generalized modus ponens state that from A' and A->B, we can
infer B', such that B' is an approximation of B (i.e. B' is a
projection of the composition A'o(A->B) ).

But how would you define logical consequence in the fuzzy case????

My first desperate attempt resulted in the following:

B' is GENERALIZED LOGICAL CONSEQUENCE of P if and only if B' is a
fuzzy equivalence with B, and that B is true in every model M of P.

Note that there are no truth values (possibility values) connected to
A' or A->B.

ANY BETTER IDEAS??

- Harry