The Constructive $\hat{I}¼$-calculus: Game Semantics and Non-Wellfounded Proof Systems

Abstract

We study a variant of the modal $\hat{I}¼$-calculus based on the constructive modal logic $\mathsf{CK}$. We define game semantics for the constructive $\hat{I}¼$-calculus and prove its equivalence to the birelational Kripke semantics. We then use the game semantics to prove the soundness and completeness of a fully-labeled non-wellfounded proof system for it. At last, we briefly describe how to adapt the game semantics and proof system to the $\hat{I}¼$-calculus over other non-classical modal logics.

Text overlap with arxiv:2308.16697