18 research outputs found

    Optimal Tableaux Method for Constructive Satisfiability Testing and Model Synthesis in the Alternating-time Temporal Logic ATL+

    Full text link
    We develop a sound, complete and practically implementable tableaux-based decision method for constructive satisfiability testing and model synthesis in the fragment ATL+ of the full Alternating time temporal logic ATL*. The method extends in an essential way a previously developed tableaux-based decision method for ATL and works in 2EXPTIME, which is the optimal worst case complexity of the satisfiability problem for ATL+ . We also discuss how suitable parametrizations and syntactic restrictions on the class of input ATL+ formulae can reduce the complexity of the satisfiability problem.Comment: 45 page

    Tableau-based decision procedures for logics of strategic ability in multi-agent systems

    Full text link
    We develop an incremental tableau-based decision procedures for the Alternating-time temporal logic ATL and some of its variants. While running within the theoretically established complexity upper bound, we claim that our tableau is practically more efficient in the average case than other decision procedures for ATL known so far. Besides, the ease of its adaptation to variants of ATL demonstrates the flexibility of the proposed procedure.Comment: To appear in ACM Transactions on Computational Logic. 48 page

    Using automata to characterise fixed point temporal logics

    Get PDF
    This work examines propositional fixed point temporal and modal logics called mu-calculi and their relationship to automata on infinite strings and trees. We use correspondences between formulae and automata to explore definability in mu-calculi and their fragments, to provide normal forms for formulae, and to prove completeness of axiomatisations. The study of such methods for describing infinitary languages is of fundamental importance to the areas of computer science dealing with non-terminating computations, in particular to the specification and verification of concurrent and reactive systems. To emphasise the close relationship between formulae of mu-calculi and alternating automata, we introduce a new first recurrence acceptance condition for automata, checking intuitively whether the first infinitely often occurring state in a run is accepting. Alternating first recurrence automata can be identified with mu-calculus formulae, and ordinary, non-alternating first recurrence automata with formulae in a particular normal form, the strongly aconjunctive form. Automata with more traditional Büchi and Rabin acceptance conditions can be easily unwound to first recurrence automata, i.e. to mu-calculus formulae. In the other direction, we describe a powerset operation for automata that corresponds to fixpoints, allowing us to translate formulae inductively to ordinary Büchi and Rabin-automata. These translations give easy proofs of the facts that Rabin-automata, the full mu-calculus, its strongly aconjunctive fragment and the monadic second-order calculus of n successors SnS are all equiexpressive, that Büchi-automata, the fixpoint alternation class Pi_2 and the strongly aconjunctive fragment of Pi_2 are similarly related, and that the weak SnS and the fixpoint-alternation-free fragment of mu-calculus also coincide. As corollaries we obtain Rabin's complementation lemma and the powerful decidability result of SnS. We then describe a direct tableau decision method for modal and linear-time mu-calculi, based on the notion of definition trees. The tableaux can be interpreted as first recurrence automata, so the construction can also be viewed as a transformation to the strongly aconjunctive normal form. Finally, we present solutions to two open axiomatisation problems, for the linear-time mu-calculus and its extension with path quantifiers. Both completeness proofs are based on transforming formulae to normal forms inspired by automata. In extending the completeness result of the linear-time mu-calculus to the version with path quantifiers, the essential problem is capturing the limit closure property of paths in an axiomatisation. To this purpose, we introduce a new \exists\nu-induction inference rule

    Branching-time logic ECTL# and its tree-style one-pass tableau: Extending fairness expressibility of ECTL+

    Get PDF
    Temporal logic has become essential for various areas in computer science, most notably for the specification and verification of hardware and software systems. For the specification purposes rich temporal languages are required that, in particular, can express fairness constraints. For linear-time logics which deal with fairness in the linear-time setting, one-pass and two-pass tableau methods have been developed. In the repository of the CTL-type branching-time setting, the well-known logics ECTL and ECTL+ were developed to explicitly deal with fairness. However, due to the syntactical restrictions, these logics can only express restricted versions of fairness. The logic CTL*, often considered as ‘the full branching-time logic’ overcomes these restrictions on expressing fairness. However, CTL* is extremely challenging for the application of verification techniques, and the tableau technique, in particular. For example, there is no one-pass tableau construction for CTL*, while one-pass tableau has an additional benefit enabling the formulation of dual sequent calculi that are often treated as more ‘natural’ being more friendly for human understanding. These two considerations lead to the following problem - are there logics that have richer expressiveness than ECTL+, allowing the formulation of a new range of fairness constraints with ‘until’ operator, yet ‘simpler’ than CTL?, and for which a one-pass tableau can be developed? Here we give a positive answer to this question, introducing a sub-logic of CTL* called ECTL#, its tree-style one-pass tableau, and an algorithm for obtaining a systematic tableau, for any given admissible branching-time formulae. We prove the termination, soundness and completeness of the method. As tree-shaped one-pass tableaux are well suited for the automation and are amenable for the implementation and for the formulation of sequent calculi. Our results also open a prospect of relevant developments of the automation and implementation of the tableau method for ECTL#, and of a dual sequent calculi.Authors have been partially supported by Spanish Project TIN2017-86727-C2-2-R, and by the University of the Basque Country under Project LoRea GIU18/182

    Branching-time logic ECTL# and its tree-style one-pass tableau: Extending fairness expressibility of ECTL+

    Get PDF
    Temporal logic has become essential for various areas in computer science, most notably for the specification and verification of hardware and software systems. For the specification purposes rich temporal languages are required that, in particular, can express fairness constraints. For linear-time logics which deal with fairness in the linear-time setting, one-pass and two-pass tableau methods have been developed. In the repository of the CTL-type branching-time setting, the well-known logics ECTL and ECTL+ were developed to explicitly deal with fairness. However, due to the syntactical restrictions, these logics can only express restricted versions of fairness. The logic CTL⋆, often considered as ‘the full branching-time logic’ overcomes these restrictions on expressing fairness. However, CTL⋆ is extremely challenging for the application of verification techniques, and the tableau technique, in particular. For example, there is no one-pass tableau construction for CTL⋆, while one-pass tableau has an additional benefit enabling the formulation of dual sequent calculi that are often treated as more ‘natural’ being more friendly for human understanding. These two considerations lead to the following problem - are there logics that have richer expressiveness than ECTL+, allowing the formulation of a new range of fairness constraints with ‘until’ operator, yet ‘simpler’ than CTL⋆, and for which a one-pass tableau can be developed? Here we give a positive answer to this question, introducing a sub-logic of CTL⋆ called ECTL#, its tree-style one-pass tableau, and an algorithm for obtaining a systematic tableau, for any given admissible branching-time formulae. We prove the termination, soundness and completeness of the method. As tree-shaped one-pass tableaux are well suited for the automation and are amenable for the implementation and for the formulation of sequent calculi. Our results also open a prospect of relevant developments of the automation and implementation of the tableau method for ECTL#, and of a dual sequent calculi

    Seeing, Knowing, doing : case studies in modal logic

    Get PDF
    Dans le domaine des jeux vidéos par exemple, surtout des jeux de rôles, les personnages virtuels perçoivent un environnement, en tirent des connaissances puis effectuent des actions selon leur besoin. De même en robotique, un robot perçoit son environnement à l'aide de capteurs/caméras, établit une base de connaissances et effectuent des mouvements etc. La description des comportements de ces agents virtuels et leurs raisonnements peut s'effectuer à l'aide d'un langage logique. Dans cette thèse, on se propose de modéliser les trois aspects "voir", "savoir" et "faire" et leurs interactions à l'aide de la logique modale. Dans une première partie, on modélise des agents dans un espace géométrique puis on définit une relation épistémique qui tient compte des positions et du regard des agents. Dans une seconde partie, on revisite la logique des actions "STIT" (see-to-it-that ou "faire en sorte que") qui permet de faire la différence entre les principes "de re" et "de dicto", contrairement à d'autres logiques modales des actions. Dans une troisième partie, on s'intéresse à modéliser quelques aspects de la théorie des jeux dans une variante de la logique "STIT" ainsi que des émotions contre-factuelles comme le regret. Tout au long de cette thèse, on s'efforcera de s'intéresser aux aspects logiques comme les complétudes des axiomatisations et la complexité du problème de satisfiabilité d'une formule logique. L'intégration des trois concepts "voir", "savoir" et "faire" dans une et une seule logique est évoquée en conclusion et reste une question ouverte.Agents are entities who perceive their environment and who perform actions. For instance in role playing video games, ennemies are agents who perceive some part of the virtual world and who can attack or launch a sortilege. Another example may concern robot assistance for disabled people: the robot perceives obstacles of the world and can alert humans or help them. Here, we try to give formal tools to model knowledge reasoning about the perception of their environment and about actions based, on modal logic. First, we give combine the standard epistemic modal logic with perception constructions of the form (agent a sees agent b). We give a semantics in terms of position and orientation of the agents in the space that can be a line (Lineland) or a plane (Flatland). Concerning Lineland, we provide a complete axiomatization and an optimal procedure for model-checking and satisfiability problem. Concerning Flatland, we show that both model-checking and satisfiability problem are decidable but the exact complexities and the axiomatization remain open problems. Thus, the logics of Lineland and Flatland are completely a new approach: their syntax is epistemic but their semantics concern spatial reasoning. Secondly, we study on the logic of agency ``see-to-it-that'' STIT made up of construction of the form [J]A standing for ``the coalition of agents J sees to it that A''. Our interest is motivated: STIT is strictly more expressive that standard modal logic for agency like Coalition Logic CL or Alternating-time Temporal Logic ATL. In CL or ATL the ``de re'' and ``de dicto'' problem is quite difficult and technical whereas if we combine STIT-operators with epistemic operators, we can solve it in a natural way. However this strong expressivity has a prize: the general version of STIT is undecidable. That is why we focus on some syntactic fragments of STIT: either we restrict the allowed coalitions J in constructions [J]A or we restrict the nesting of modal STIT-operators. We provide axiomatizations and complexity results. Finally, we give flavour to epistemic modal logic by adding STIT-operators. The logic STIT is suitable to express counterfactual statements like ``agent a could have choosen an action such that A have been true''. Thus we show how to model counterfactual emotions like regret, rejoicing, disappointment and elation in this framework. We also model epistemic games by adapting the logic STIT by giving explicitely names of actions in the language. In this framework, we can model the notion of rational agents but other kind of behaviour like altruism etc., Nash equilibrium and iterated deletion of strictly dominated strategies

    Advanced reduction techniques for model checking

    Get PDF

    Computer Science Logic 2018: CSL 2018, September 4-8, 2018, Birmingham, United Kingdom

    Get PDF

    Synthesis of asynchronous distributed systems from global specifications

    Get PDF
    The synthesis problem asks whether there exists an implementation for a given formal specification and derives such an implementation if it exists. This approach enables engineers to think on a more abstract level about what a system should achieve instead of how it should accomplish its goal. The synthesis problem is often represented by a game between system players and environment players. Petri games define the synthesis problem for asynchronous distributed systems with causal memory. So far, decidability results for Petri games are mainly obtained for local winning conditions, which is limiting as global properties like mutual exclusion cannot be expressed. In this thesis, we make two contributions. First, we present decidability and undecidability results for Petri games with global winning conditions. The global safety winning condition of bad markings defines markings that the players have to avoid. We prove that the existence of a winning strategy for the system players in Petri games with a bounded number of system players, at most one environment player, and bad markings is decidable. The global liveness winning condition of good markings defines markings that the players have to reach. We prove that the existence of a winning strategy for the system players in Petri games with at least two system players, at least three environment players, and good markings is undecidable. Second, we present semi-decision procedures to find winning strategies for the system players in Petri games with global winning conditions and without restrictions on the distribution of players. The distributed nature of Petri games is employed by proposing encodings with true concurrency. We implement the semi-decision procedures in a corresponding tool.Das Syntheseproblem stellt die Frage, ob eine Implementierung f ¨ur eine Spezifikation existiert, und generiert eine solche Implementierung, falls sie existiert. Diese Vorgehensweise erlaubt es Programmierenden sich mehr darauf zu konzentrieren, was ein System erreichen soll, und weniger darauf, wie die Spezifikation erf ¨ ullt werden soll. Das Syntheseproblem wird oft als Spiel zwischen einem System- und einem Umgebungsspieler dargestellt. Petri-Spiele definieren das Syntheseproblem f ¨ur asynchrone verteilte Systeme mit kausalem Speicher. Bisher wurden Resultate bez¨uglich der Entscheidbarkeit von Petri-Spiele meist f ¨ur lokale Gewinnbedingungen gefunden. In dieser Arbeit pr¨asentieren wir zuerst Resultate bez¨uglich der Entscheidbarkeit und Unentscheidbarkeit von Petri-Spielen mit globalen Gewinnbedingungen. Wir beweisen, dass die Existenz einer gewinnenden Strategie f ¨ur die Systemspieler in Petri- Spielen mit einer beschr¨ankten Anzahl an Systemspielern, h¨ochstens einem Umgebungsspieler und schlechten Markierungen entscheidbar ist. Wir beweisen ebenfalls, dass die Existenz einer gewinnenden Strategie f ¨ur die Systemspieler in Petri-Spielen mit mindestens zwei Systemspielern, mindestens drei Umgebungsspielern und guten Markierungen unentscheidbar ist. Danach pr¨asentieren wir Semi-Entscheidungsprozeduren, um gewinnende Strategien f ¨ur die Systemspieler in Petri-Spielen mit globalen Gewinnbedingungen und ohne Restriktionen f ¨ur die Verteilung von Spielern zu finden. Wir benutzen die verteilte Natur von Petri-Spielen, indem wir Enkodierungen einf ¨uhren, die Nebenl¨aufigkeit ausnutzen. Die Semi-Entscheidungsprozeduren sind in einem entsprechenden Tool implementiert
    corecore