The alternating-time µ-calculus with disjunctive explicit strategies

Merlin Göttlinger, Lutz Schröder, Dirk Pattinson

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    Abstract

    Alternating-time temporal logic (ATL) and its extensions, including the alternating-time µ-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 µ-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 non-determinism 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 ∩ 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.

    Original languageEnglish
    Title of host publication29th EACSL Annual Conference on Computer Science Logic, CSL 2021
    EditorsChristel Baier, Jean Goubault-Larrecq
    PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
    ISBN (Electronic)9783959771757
    DOIs
    Publication statusPublished - Jan 2021
    Event29th EACSL Annual Conference on Computer Science Logic, CSL 2021 - Virtual, Ljubljana, Slovenia
    Duration: 25 Jan 202128 Jan 2021

    Publication series

    NameLeibniz International Proceedings in Informatics, LIPIcs
    Volume183
    ISSN (Print)1868-8969

    Conference

    Conference29th EACSL Annual Conference on Computer Science Logic, CSL 2021
    Country/TerritorySlovenia
    CityVirtual, Ljubljana
    Period25/01/2128/01/21

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