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A Propositional Dynamic Logic for Instantial Neighborhood Semantics


We propose a new perspective on logics of computation by combining instantial neighborhood logic \(\mathsf {INL}\) with bisimulation safe operations adapted from \(\mathsf {PDL}\). \(\mathsf {INL}\) 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 \(\mathsf {INL}\). We also prove that our extended logic \(\mathsf {IPDL}\) 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 \(\mathsf {IPDL}\), and establish its finite model property and decidability.


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We thank the referee for valuable feedback and for spotting an error in the original version of the proof of Theorem 7. We also thank a number of colleagues for helpful discussions on earlier versions of the manuscript, where in particular we wish to mention Valentin Goranko, Helle Hansen, Tadeusz Litak and Lutz Schröder.

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Correspondence to Sebastian Enqvist.

Additional information

Presented by Heinrich Wansing; Received December 16, 2017

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van Benthem, J., Bezhanishvili, N. & Enqvist, S. A Propositional Dynamic Logic for Instantial Neighborhood Semantics. Stud Logica 107, 719–751 (2019).

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  • Dynamic logic
  • Game logic
  • Neighborhood models
  • Instantial neighborhood logic