Propositional dynamic logic with Belnapian truth values

2016/08/22 by Igor Sedlár, Sedlár, Igor · 1 citation
Computer Science · #Advanced Algebra and Logic #F.3.1 #F.4.1 #FOS: Computer and information sciences #Formal Methods in Verification #I.2.4 #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge

paper · pdf · doi:10.48550/arxiv.1608.06084

openalex publication_date 2016/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce BPDL, a combination of propositional dynamic logic PDL with the basic four-valued modal logic BK studied by Odintsov and Wansing (`Modal logics with Belnapian truth values', J. Appl. Non-Class. Log. 20, 279--301 (2010)). We modify the standard arguments based on canonical models and filtration to suit the four-valued context and prove weak completeness and decidability of BPDL.

Citations

• Propositional dynamic logic of regular programs

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• Many-valued coalgebraic dynamic logics: Safety and strong completeness via reducibility

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