The Alternating-Time \mu-Calculus With Disjunctive Explicit Strategies

Alternating-time temporal logic (ATL) and its extensions, including the alternating-time $\mu$-calculus (AMC), serve the specification of the strategic abilities of coalitions of agents in concurrent game structures. The key ingredient of the logic are path quantifiers specifying that some coalition of agents has a joint strategy to enforce a given goal. This basic setup has been extended to let some of the agents (revocably) commit to using certain named strategies, as in ATL with explicit strategies (ATLES). In the present work, we extend ATLES with fixpoint operators and strategy disjunction, arriving at the alternating-time $\mu$-calculus with disjunctive explicit strategies (AMCDES), which allows for a more flexible formulation of temporal properties (e.g. fairness) and, through strategy disjunction, a form of controlled nondeterminism in commitments. Our main result is an ExpTime upper bound for satisfiability checking (which is thus ExpTime-complete). We also prove upper bounds QP (quasipolynomial time) and NP $\cap$ coNP for model checking under fixed interpretations of explicit strategies, and NP under open interpretation. Our key technical tool is a treatment of the AMCDES within the generic framework of coalgebraic logic, which in particular reduces the analysis of most reasoning tasks to the treatment of a very simple one-step logic featuring only propositional operators and next-step operators without nesting; we give a new model construction principle for this one-step logic that relies on a set-valued variant of first-order resolution.Comment: Full version with appendix as well as corrected set-valued resolution metho

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

Towards an Updatable Strategy Logic

This article is about temporal multi-agent logics. Several of these formalisms have been already presented (ATL-ATL*, ATLsc, SL). They enable to express the capacities of agents in a system to ensure the satisfaction of temporal properties. Particularly, SL and ATLsc enable several agents to interact in a context mixing the different strategies they play in a semantical game. We generalize this possibility by proposing a new formalism, Updating Strategy Logic (USL). In USL, an agent can also refine its own strategy. The gain in expressive power rises the notion of "sustainable capacities" for agents. USL is built from SL. It mainly brings to SL the two following modifications: semantically, the successor of a given state is not uniquely determined by the data of one choice from each agent. Syntactically, we introduce in the language an operator, called an "unbinder", which explicitely deletes the binding of a strategy to an agent. We show that USL is strictly more expressive than SL.Comment: In Proceedings SR 2013, arXiv:1303.007

MCMAS-SLK: A Model Checker for the Verification of Strategy Logic Specifications

We introduce MCMAS-SLK, a BDD-based model checker for the verification of systems against specifications expressed in a novel, epistemic variant of strategy logic. We give syntax and semantics of the specification language and introduce a labelling algorithm for epistemic and strategy logic modalities. We provide details of the checker which can also be used for synthesising agents' strategies so that a specification is satisfied by the system. We evaluate the efficiency of the implementation by discussing the results obtained for the dining cryptographers protocol and a variant of the cake-cutting problem

Refining and Delegating Strategic Ability in ATL

We propose extending Alternating-time Temporal Logic (ATL) by an operator <i refines-to G> F to express that agent i can distribute its powers to a set of sub-agents G in a way which satisfies ATL condition f on the strategic ability of the coalitions they may form, possibly together with others agents. We prove the decidability of model-checking of formulas whose subformulas with this operator as the main connective have the form ...<i_m refines-to G_m> f, with no further occurrences of this operator in f.Comment: In Proceedings SR 2014, arXiv:1404.041