Finitely-valued propositional dynamic logics

0537049 - ÚI 2021 RIV GB eng C - Konferenční příspěvek (zahraniční konf.)
Sedlár, Igor
Finitely-valued propositional dynamic logics.
Advances in Modal Logic. London: College Publications, 2020 - (Olivetti, N.; Verbrugge, R.; Negri, S.; Sandu, G.), s. 561-579. ISBN 978-1-84890-341-8.
[AiML 2020: Conference on Advances in Modal Logic /14./. Helsinki / Online (FI), 24.08.2020-28.08.2020]
Grant CEP: GA ČR(CZ) GJ18-19162Y
Institucionální podpora: RVO:67985807
Klíčová slova: FL-algebras * Many-valued modal logic * Propositional Dynamic Logic * Residuated lattices * Substructural logics * Weighted structures
Obor OECD: Pure mathematics

We study a many-valued generalization of Propositional Dynamic Logic where formulas in states and accessibility relations between states of a Kripke model are evaluated in a finite FL-algebra. One natural interpretation of this framework is related to reasoning about costs of performing structured actions. We prove that PDL over any finite FL-algebra is decidable. We also establish a general completeness result for a class of PDLs based on commutative integral FL-algebras with canonical constants.
Trvalý link: http://hdl.handle.net/11104/0314800