Supervaluations, truth, and intuitionistic logic

Abstract

The supervaluationist approach to fixed-point semantics is, arguably, the most celebrated and studied competitor to the Strong Kleene approach within Kripkean truth. In this paper, we show how to obtain supervaluationist fixed-point theories of truth for intuitionistic logic. In particular, we show how to do supervaluations over Kripke structures for intuitionistic logic, and we obtain the corresponding theories of truth, both semantic and axiomatic. Furthermore, we technically compare our approach with previous attempts to formalize Kripkean supervaluational theories over possible-world semantics. Finally, we show that, unlike in the case of classical logic, a fixed-point theory over intuitionistic logic can be given that is both supervaluational and highly compositional in nature.