PP-2016-28: Modal Logics of Sabotage Revisited

PP-2016-28: Aucher, Guillaume and and Davide Grossi, Johan van Benthem (2016) Modal Logics of Sabotage Revisited. [Report]

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Abstract

Sabotage modal logic was proposed in 2003 as a format for analyzing games that modify the graphs they are played on. We investigate some model-theoretic and proof-theoretic aspects of sabotage modal logic, which has largely come to be viewed as an early dynamic logic of graph change. Our first contribution is a characterization theorem for sabotage modal logic as a fragment of first-order logic which is invariant with respect to a natural notion of ‘sabotage bisimulation’. Our second contribution is a sound and complete tableau method for analyzing reasoning in sabotage modal logic. Next, we identify and briefly explore a number of open research problems concerning sabotage modal logic that illuminate its complexity, placing it within the current landscape of modal logics that analyze model update, including new `stepwise' and 'local' variants of dynamic-epistemic logics. Finally, returning to the original motivation of sabotage, we ex[lore new fixed-point logics for network games that pose some delicate challenges of combining mu-calculi with dynamic modalities for model change. Note: This is an extended version of a paper presented at LORI Taipei 2015, which will appear in the "Knowledge and Rationality" subseries of "Synthese".

Item Type: Report
Report Nr: PP-2016-28
Series Name: Prepublication (PP) Series
Year: 2016
Uncontrolled Keywords: sabotage game, graph games, modal logic, model change, complexity, dynamic-epistemic logic
Subjects: Logic
Depositing User: Johan van Benthem
Date Deposited: 22 Dec 2017 15:24
Last Modified: 22 Dec 2017 15:24
URI: https://eprints.illc.uva.nl/id/eprint/1581

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