Marco Cerami - Witnessed and quasi-witnessed models in first order fuzzy logic
Channel: Mathematical Logic UFBA
Date: 29/05/2015

Seminar given by Marco Cerami at the Instituto de Matemática of the Universidade Federal da Bahia - Brazil.
May 27, 2015

Abstract:
The idea behind quantified formulas in first order logic is that of expressing the fact that some (resp. all) model domain elements instantiate the formula to be quantified. Call this instantiating element a “witness” of the quantified formula. In this sense the satisfaction of a quantified formula has a naturally bi-valued range. In the case of classical first order logic this notion coincides with the supremum (resp. infimum) of the instantiations of the formula to be quantified, among the model domain elements. In order to maintain a multi-valued evaluation, the semantics of quantified formulas in first order fuzzy logic is defined by means of the supremum (resp. infimum) of the instantiations of the formula to be quantified. But when the algebra of truth values is infinite, this supremum (resp. infimum) does not need to coincide with the value of the formula instantiated by any domain element. That is, a quantified formula does not need to have a witness. In this talk we are giving an account on under which conditions and until which extent some known first order fuzzy logics have models that guarantee a witness for quantified formulas.