A Decidable Fragment of Strategy Logic
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by
Fabio Mogavero, Aniello Murano, Giuseppe Perelli, Moshe Y. Vardi
2012
Abstract
Strategy Logic (SL, for short) has been recently 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 to be very powerful, subsuming all major previously studied modal logics
for strategic reasoning, including ATL, ATL*, and the like. Unfortunately, due
to its expressiveness, SL has a non-elementarily decidable model-checking
problem and a highly undecidable satisfiability problem, specifically,
Σ_1^1-Hard. In order to obtain a decidable sublogic, we introduce
and study here One-Goal Strategy Logic (SL[1G], for short). This logic 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. SL[1G] is known to have an elementarily
decidable model-checking problem. Here we prove that, unlike SL, it has the
bounded tree-model property and its satisfiability problem is decidable in
2ExpTime, thus not harder than the one for ATL*.
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