A strong completeness theorem in intuitionistic quantified modal logic

Abstract

Based on the intuitionistic first order predicate calculusH given by Thomason with the modal machinery of MIPC put forward by Prior this paper obtains the intuitionistic quantified modal logic system MIPC*, gives it a semantic interpretation and proves its strong (thus also weak) completeness theorem and soundness theorem with respect to that semantic. Since Zorn lemma plays a decisive role in our discussion, methodologically, it was even farther from the intuitionistic point of view than Thomason's result.