PP-2017-25: A New Game Equivalence and Its Modal Logic

PP-2017-25: van Benthem, Johan and Bezhanishvili, Nick and Enqvist, Sebastian (2017) A New Game Equivalence and Its Modal Logic. [Pre-print]

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Abstract

We revisit the crucial issue of natural game equivalences, and semantics of game logics based on these. We present reasons for investigating finer concepts of game equivalence than equality of standard powers, though staying short of modal bisimulation. Concretely, we propose a more fine-grained notion of equality of ‘basic powers’ which record what players can force plus what they leave to others to do, a crucial feature of interaction. This notion is closer to game-theoretic strategic form, as we explain in detail, while remaining amenable to logical analysis. We determine the properties of basic powers via a new representation theorem, find a matching ‘instantial neighborhood game logic’, and show how our analysis can be extended to a new game algebra and dynamic game logic. We also take on board imperfect information and epistemic logic in a systematic manner, and explore a few connections with other logics of games. The extended final version of this paper has appeared in the "Journal of Philosophical Logic" on-line, Autumn 2018.

Item Type:	Pre-print
Report Nr:	PP-2017-25
Series Name:	Prepublication (PP) Series
Year:	2017
Subjects:	Computation Logic Mathematics
Depositing User:	Johan van Benthem
Date Deposited:	05 Feb 2021 19:19
Last Modified:	05 Feb 2021 19:19
URI:	https://eprints.illc.uva.nl/id/eprint/1772

Available Versions of this Item

• A New Game Equivalence and Its Modal Logic. (deposited 23 Dec 2017 13:01)
  • A New Game Equivalence and Its Modal Logic. (deposited 24 Jan 2019 14:08)
    • A New Game Equivalence and Its Modal Logic. (deposited 05 Feb 2021 19:19) [Currently Displayed]

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