Giuseppe Perelli — Page 2

arXiv2012

A Decidable Fragment of Strategy Logic

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*.

cs.LO↗

arXiv2012

Reasoning About Strategies: On the Model-Checking Problem

In open systems verification, to formally check for reliability, one needs an appropriate formalism to model the interaction between agents and express the correctness of the system no matter how the environment behaves. An important contribution in this context is given by modal logics for strategic ability, in the setting of multi-agent games, such as ATL, ATL\star, and the like. Recently, Chatterjee, Henzinger, and Piterman introduced Strategy Logic, which we denote here by CHP-SL, with the aim of getting a powerful framework for reasoning explicitly about strategies. CHP-SL is obtained by using first-order quantifications over strategies and has been investigated in the very specific setting of two-agents turned-based games, where a non-elementary model-checking algorithm has been provided. While CHP-SL is a very expressive logic, we claim that it does not fully capture the strategic aspects of multi-agent systems. In this paper, we introduce and study a more general strategy logic, denoted SL, for reasoning about strategies in multi-agent concurrent games. We prove that SL includes CHP-SL, while maintaining a decidable model-checking problem. In particular, the algorithm we propose is computationally not harder than the best one known for CHP-SL. Moreover, we prove that such a problem for SL is NonElementarySpace-hard. This negative result has spurred us to investigate here syntactic fragments of SL, strictly subsuming ATL\star, with the hope of obtaining an elementary model-checking problem. Among the others, we study the sublogics SL[NG], SL[BG], and SL[1G]. They encompass formulas in a special prenex normal form having, respectively, nested temporal goals, Boolean combinations of goals and, a single goal at a time. About these logics, we prove that the model-checking problem for SL[1G] is 2ExpTime-complete, thus not harder than the one for ATL\star.

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