On models in fuzzy propositional logic

Authors:
Jorma K. Mattila
Affiliations:
Laboratory of Applied Mathematics, Lappeenranta University of Technology
Venue:
KES'06 Proceedings of the 10th international conference on Knowledge-Based Intelligent Information and Engineering Systems - Volume Part III
Year:
2006

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Abstract

A model theory of fuzzy propositional logic is considered. The basic frame for fuzzy propositional logics are Zadeh-algebras, i.e., special quasi-Boolean algebras, where valuation functions are universes of these algebras. There are two levels of truth-values, numerical (usually the unit interval[0,1], or in general, a lattice L) and linguistic. Linguistic truth-values are fuzzy subsets of the set of numerical truth-values. Fuzzy model is defined based on numerical truth-values, i.e. it is the set of designated truth-values. Its linguistic label is true. Truth conditions and the concepts validity, satisfiability, refutability, and invalidity are considered.