报告人: 钟盛阳

题目：Propositional Logic and Modal Logic - A Connection via Relational Semantics 

时间：2022/02/22 15:10-18:00

地点：三教 201

摘要: In this talk, by slightly generalizing an observation of Dalla Chiara and Giuntini in their chapter on quantum logic in Handbook of Philosophical Logic, we propose a relational semantics for propositional language with negation and conjunction, which unifies the relational semantics of intuitionistic logic and that of ortho-logic. We study the semantic and syntactic consequence relations and prove the soundness and completeness theorems for five propositional logics BL, PL, IL, OL and CL. Moreover, we prove that they can be translated into the modal logics K, T, S4, KTB and S5, respectively, and thus establish a systematic connection between propositional logics and modal logics. The talk ends with a discussion about the possibility and difficulty of incorporating disjunction into our framework.