Mogavero, Fabio and Murano, Aniello and Perelli, Giuseppe and Vardi, Moshe Y. - Reasoning about Strategies: on the Satisfiability Problem

lmcs:3204 - Logical Methods in Computer Science, March 17, 2017, Volume 13, Issue 1
Reasoning about Strategies: on the Satisfiability Problem

Authors: Mogavero, Fabio and Murano, Aniello and Perelli, Giuseppe and Vardi, Moshe Y.

Strategy Logic (SL, for short) has been introduced by Mogavero, Murano, and Vardi as a useful formalism for reasoning explicitly about strategies, as first-order objects, in multi-agent concurrent games. This logic turns out to be very powerful, subsuming all major previously studied modal logics for strategic reasoning, including ATL, ATL*, and the like. Unfortunately, due to its high expressiveness, SL has a non-elementarily decidable model-checking problem and the satisfiability question is undecidable, specifically Sigma_1^1. In order to obtain a decidable sublogic, we introduce and study here One-Goal Strategy Logic (SL[1G], for short). This is a syntactic fragment of SL, strictly subsuming ATL*, which encompasses formulas in prenex normal form having a single temporal goal at a time, for every strategy quantification of agents. We prove that, unlike SL, SL[1G] has the bounded tree-model property and its satisfiability problem is decidable in 2ExpTime, thus not harder than the one for ATL*.


Source : oai:arXiv.org:1611.08541
DOI : 10.23638/LMCS-13(1:9)2017
Volume: Volume 13, Issue 1
Published on: March 17, 2017
Submitted on: March 17, 2017
Keywords: Computer Science - Logic in Computer Science,F.3.1,F.4.1


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