Propositional Dynamic Logic with Belnapian Truth Values

Authors: Igor Sedlár
Publication year: 2016
Publication type: Konferenční příspěvek (mezinárodní konf.)
Periodical: Advances in Modal Logic
Projects: Center of excellence - Institute for theoretical computer science (CE-ITI)
Bibliographic citation: SEDLÁR, Igor. Propositional Dynamic Logic with Belnapian Truth Values. In: BEKLEMISHEV, L., DEMRI, S., MÁTÉ, A., eds. Advances in Modal Logic. Vol. 11. London: College Publications, 2016, S. 503-519. ISBN 978-1-84890-201-5. Dostupné z: http://www.aiml.net/volumes/volume11/
ID: 465841

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.