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What Makes Atl* Decidable? A Decidable Fragment of Strategy Logic

  • Fabio Mogavero
  • Aniello Murano
  • Giuseppe Perelli
  • Moshe Y. Vardi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7454)

Abstract

Strategy Logic (Sl, for short) has been recently introduced by Mogavero, Murano, and Vardi as a formalism for reasoning explicitly about strategies, as first-order objects, in multi-agent concurrent games. This logic turns out to be very powerful, strictly subsuming all major previously studied modal logics for strategic reasoning, including Atl, Atl*, and the like. The price that one has to pay for the expressiveness of Sl is the lack of important model-theoretic properties and an increased complexity of decision problems. In particular, Sl does not have the bounded-tree model property and the related satisfiability problem is highly undecidable while for Atl* it is 2ExpTime-complete. An obvious question that arises is then what makes Atl* decidable. Understanding this should enable us to identify decidable fragments of Sl. We focus, in this work, on the limitation of Atl* to allow only one temporal goal for each strategic assertion and study the fragment of Sl with the same restriction. Specifically, we introduce and study the syntactic fragment One-Goal Strategy Logic (Sl[1g], for short), which consists of formulas in prenex normal form having a single temporal goal at a time for every strategy quantification of agents. We show that Sl[1g] is strictly more expressive than Atl*. Our main result is that Sl[1g] has the bounded tree-model property and its satisfiability problem is 2ExpTime-complete, as it is for Atl*.

Keywords

Modal Logic Atomic Proposition Strategy Logic Tree Automaton Universal Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Fabio Mogavero
    • 1
  • Aniello Murano
    • 1
  • Giuseppe Perelli
    • 1
  • Moshe Y. Vardi
    • 2
  1. 1.Università degli Studi di Napoli ”Federico II”NapoliItaly
  2. 2.Rice UniversityHoustonUSA

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