A Criticism of Kripke’s Semantic for Intuitionistic Logic

Abstract

This note aims to examine critically Kripke’s semantics for propositional intuitionistic logic. Kripke’s semantic is extensionally correct with respect to propositional intuitionistic logic, that is, the calculus is sound and complete with respect to the semantics. The fragment of propositional intuitionist logic containing disjunction and implication is also sound and complete with respect to the respective semantical clauses. However, we´ll argue, Kripke semantics is intensionallymisleading, since Kripke’ssemantical implication clause is intensionallymisleading. And the problem can be exemplified when we consider the fragment with disjunction and implication.