Mathematical fuzzy logic - what it can learn from Mostowski and Rasiowa.

Petr Hajek, Prague (Abstract.)

Mathematical fuzzy logic is understood as a collection of symbolic (formal)
systems with a comparative notion of truth most important systems being
t-norm based (truth-function of conjunction being a left-continuous t-norm).
Both propositional and predicate fuzzy logic has been developed (see [1]);
a characteristic feature is double semantics - standard with the set of truth
degrees being the real unit interval, and general with a certain variety
of algebras of truth functions (particular residuated lattices).
   It turns out that several ideas, notions and constructions vital for the
development of fuzzy predicate logic are found in older works by Mostowski
and Rasiowa, as axiomatization of some semantical notions [2], use
of generalized quantifiers [3] and then notion of a safe interpretation
of predicate language [4]. The talk will survey basic facts of fuzzhy predicate
calculi, referring to related works by Mostowski and Rasiowa.

  References:
[1] P. Hajek: metamathematics of fuzzy logic. Kluwer 1998. 
[2] A. Mostowski: Axiomatizability of some many valued predicate calculi. 
Fund. Math. 50 (1961), 165-190. 
[3] A. Mostowski: On a generalization of quantifiers.
Fund. Math. 44 (1957) 12.36 
[4] H. Rasiowa: An algebraic approach to non-classical logics.