Studia Logica 107 (4):719-751 (2019)

Authors
Nick Bezhanishvili
University of Amsterdam
Johan Van Benthem
University of Amsterdam
Abstract
We propose a new perspective on logics of computation by combining instantial neighborhood logic $$\mathsf {INL}$$ INL with bisimulation safe operations adapted from $$\mathsf {PDL}$$ PDL. $$\mathsf {INL}$$ 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 $$\mathsf {INL}$$ INL. We also prove that our extended logic $$\mathsf {IPDL}$$ 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 $$\mathsf {IPDL}$$ IPDL, and establish its finite model property and decidability.
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DOI 10.1007/s11225-018-9825-5
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