Substructural logics with a reflexive transitive closure modality

0477326 - FLÚ 2018 RIV DE eng C - Konferenční příspěvek (zahraniční konf.)
Sedlár, Igor
Substructural logics with a reflexive transitive closure modality.
Logic, Language, Information, and Computation. Berlin: Springer, 2017 - (Kennedy, J.; de Queiroz, R.), s. 349-357. Lecture Notes in Computer Science, 10388. ISBN 978-3-662-55385-5. ISSN 0302-9743.
[International Workshop, WoLLIC 2017 /24./. London (GB), 18.07.2017-21.07.2017]
Grant CEP: GA ČR(CZ) GC16-07954J
Institucionální podpora: RVO:67985955
Klíčová slova: substructural logics * modal logic * reflexive transitive closure * intuitionistic modal logic
Obor OECD: Philosophy, History and Philosophy of science and technology

Reflexive transitive closure modalities represent a number of important notions, such as common knowledge in a group of agents or non-deterministic iteration of actions. Normal modal logics with such modalities are well-explored but weaker logics are not. We add a reflexive transitive closure box modality to the modal non-associative commutative full Lambek calculus with a simple negation. Decidability and weak completeness of the resulting system are established and extensions of the results to stronger substructural logics are discussed. As a special case, we obtain decidability and weak completeness for intuitionistic modal logic with the reflexive transitive closure box.
Trvalý link: http://hdl.handle.net/11104/0273701