On an Inferential Semantics for Intuitionistic Sentential Logic

Abstract: Sandqvist's base-extension semantics (B-eS) for intuitionistic sentential logic grounds meaning relative to bases (rather than, say, models), which are arbitrary sets of permitted inferences over sentences. While his soundness proof is standard, his completeness proof, is quite unusual. It closely parallels a method introduced much earlier by Mints, who developed a resolution-based approach to intuitionistic logic using a systematic translation of formulas into sentential counterparts. In this short note, we highlight the connection between these two approaches and show that the soundness and completeness of B-eS follow directly from Mints' theorem. While the result is modest, it reinforces the relevance of proof-search to proof-theoretic semantics and suggests that resolution methods have a deeper conceptual role in constructive reasoning than is often acknowledged.