Multi-Valued Models for Intuitionistic Logic
Alexander Sakharov · 2025
Models for intuitionistic logic involve sets that are different from the sets of truth values. Traditional multi-valued models are introduced in this paper. The truth values of implication and negation formulas are recursively defined so that they are dependent on all subformulas. Mimimum and maximum are employed as the truth functions for conjunction and disjunction, respectively. Supremum and infimum define the truth values of quantifier formulas and formulas with free variables. As a result, multi-valued models are defined for a variety of sets of truth values. For every such set, these models are sound and complete for intuitionistic first-order logic.