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A Propositional Dynamic Logic for Instantial Neighborhood Semantics
Stockholm University, Faculty of Humanities, Department of Philosophy.
Number of Authors: 32019 (English)In: Studia Logica: An International Journal for Symbolic Logic, ISSN 0039-3215, E-ISSN 1572-8730, Vol. 107, no 4, p. 719-751Article in journal (Refereed) Published
Abstract [en]

We propose a new perspective on logics of computation by combining instantial neighborhood logic INL with bisimulation safe operations adapted from PDL. INL is a recent modal logic, based on an extended neighborhood semantics which permits quantification over individual neighborhoods plus their contents. This system has a natural interpretation as a logic of computation in open systems. Motivated by this interpretation, we show that a number of familiar program constructors can be adapted to instantial neighborhood semantics to preserve invariance for instantial neighborhood bisimulations, the appropriate bisimulation concept for INL. We also prove that our extended logic IPDL is a conservative extension of dual-free game logic, and its semantics generalizes the monotone neighborhood semantics of game logic. Finally, we provide a sound and complete system of axioms for IPDL, and establish its finite model property and decidability.

Place, publisher, year, edition, pages
2019. Vol. 107, no 4, p. 719-751
Keywords [en]
Dynamic logic, Game logic, Neighborhood models, Instantial neighborhood logic
National Category
Mathematics Computer and Information Sciences
Identifiers
URN: urn:nbn:se:su:diva-171975DOI: 10.1007/s11225-018-9825-5ISI: 000475880700007OAI: oai:DiVA.org:su-171975DiVA, id: diva2:1348339
Available from: 2019-09-04 Created: 2019-09-04 Last updated: 2019-09-04Bibliographically approved

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