Model-Characterizing Formulas and Normal Forms in Godel Logics

Abstract

This paper focuses on three kinds of normal forms: the weak conjunctive normal form, the weak disjunctive normal form and the weak implicational normal form. The existence of these normal forms in Godel logics is investigated, and two kinds of reduction methods for them are presented, one of which is based on model-characterizing formulas and the other on rewriting systems. As byproducts of these investigations, three kinds of model-characterizing formulas are obtained. In the end, the complexities of reductions to these normal forms are also studied.