Optimal methods for reasoning about actions and plans in multi-agent systems

Cet travail présente une solution au problème du décor inférenciel. Nous réalisons cela en donnant une éducation polynomiale d'un fragment du calcul des situations vers la logique épistémique dynamique (DEL). En suite, une nouvelle méthode de preuve pour DEL, dont la complexité algorithmique est inférieure à celle de la méthode de Reiter pour le calcul de situations, est proposée. Ce travail présente aussi une nouvelle logique pour raisonner sur les actions. Cette logique permet d'exprimer formellement "qu'il existe une suite d'action conduisant au but". L'idée étant que, avec la quantification sur les actions, la planification devient un problème de validité. Une axiomatisation et quelques résultats d'expressivité sont donnés, ainsi qu'une méthode de preuve basée sur les tableaux sémantiques.This work presents a solution to the inferential frame problem. We do so by providing a polynomial reduction from a fragment of situation calculus to espistemic dynamic logic (DEL). Then, a novel proof method for DEL, such that the computational complexity is much lower than that of Retier's proof method for situation caluculs, is proposed. This work also presents a new logic for reasoning about actions. This logic allows to formally express that "there exists a sequence of actions that leads to the goal". The idea is that, with quantification over actions, planning can become a validity problem. An axiomatisation and some expressivity results are provided, as well as a proof method based on sematic tableaux

Complexity and Expressivity of Branching- and Alternating-Time Temporal Logics with Finitely Many Variables

We show that Branching-time temporal logics CTL and CTL*, as well as Alternating-time temporal logics ATL and ATL*, are as semantically expressive in the language with a single propositional variable as they are in the full language, i.e., with an unlimited supply of propositional variables. It follows that satisfiability for CTL, as well as for ATL, with a single variable is EXPTIME-complete, while satisfiability for CTL*, as well as for ATL*, with a single variable is 2EXPTIME-complete,--i.e., for these logics, the satisfiability for formulas with only one variable is as hard as satisfiability for arbitrary formulas.Comment: Prefinal version of the published pape

New Directions in Model Checking Dynamic Epistemic Logic

Dynamic Epistemic Logic (DEL) can model complex information scenarios in a way that appeals to logicians. However, its existing implementations are based on explicit model checking which can only deal with small models, so we do not know how DEL performs for larger and real-world problems. For temporal logics, in contrast, symbolic model checking has been developed and successfully applied, for example in protocol and hardware verification. Symbolic model checkers for temporal logics are very efficient and can deal with very large models. In this thesis we build a bridge: new faithful representations of DEL models as so-called knowledge and belief structures that allow for symbolic model checking. For complex epistemic and factual change we introduce transformers, a symbolic replacement for action models. Besides a detailed explanation of the theory, we present SMCDEL: a Haskell implementation of symbolic model checking for DEL using Binary Decision Diagrams. Our new methods can solve well-known benchmark problems in epistemic scenarios much faster than existing methods for DEL. We also compare its performance to to existing model checkers for temporal logics and show that DEL can compete with established frameworks. We zoom in on two specific variants of DEL for concrete applications. First, we introduce Public Inspection Logic, a new framework for the knowledge of variables and its dynamics. Second, we study the dynamic gossip problem and how it can be analyzed with epistemic logic. We show that existing gossip protocols can be improved, but that no perfect strengthening of "Learn New Secrets" exists

Relation-changing modal logics

Tesis (Doctor en Cs. de la Computación)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía y Física, 2014.En esta tesis investigamos operadores modales dinámicos que pueden cambiar el modelo durante la evaluación de una fórmula. En particular, extendemos el lenguaje modal básico con modalidades que son capaces de invertir, borrar o agregar pares de elementos relacionados. Estudiamos la versión local de los operadores (es decir,la realización de modificaciones desde el punto de evaluación) y la versión global(cambiar arbitrariamente el modelo). Investigamos varias propiedades de los lenguajes introducidos, desde un punto de vista abstracto. En primer lugar, se introduce la semántica formal de los modificadores de modelo, e inmediatamente se introduce una noción de bisimulación. Las bisimulaciones son una herramienta importante para investigar el poder expresivo de los lenguajes introducidos en esta tesis. Se demostró que todas los lenguajes son incomparables entre sí en términos de poder expresivo (a excepción de los dos versiones de swap, aunque conjeturamos que también ́en son incomparables). Continuamos por investigar el comportamiento computacional de este tipo de operadores. En primer lugar, demostramos que el problema de satisfactibilidad para las versiones locales de las lógicas que cambian la relación que investigamos es indecidible. También demostramos que el problema de model checking es PSPACE-completo para las seis lógicas. Finalmente, investigamos model checking fijando el modelo y fijando la fórmula (problemas conocidos como complejidad de fórmula y complejidad del programa, respectivamente). Es posible también definir métodos para comprobar satisfactibilidad que no necesariamente terminan. Introducimos métodos de tableau para las lógicas que cambian las relaciones y demostramos que todos estos métodos son correctos y completos y mostramos algunos aplicaciones. En la última parte de la tesis, se discute un contexto concreto en el que pueden aplicarse las lógicas modales que cambian la relación: Lógicas Dinámicas Epistémicas (DEL, por las siglas en inglés). Definimos una lógica que cambia la relación capaz de codificar DEL, e investigamos su comportamiento computacional.In this thesis we study dynamic modal operators that can change the model during the evaluation of a formula. In particular, we extend the basic modal language with modalities that are able to swap, delete or add pairs of related elements of the domain. We call the resulting logics Relation-Changing Modal Logics. We study local version of the operators (performing modifications from the evaluation point) and global version (changing arbitrarily edges in the model). We investigate several properties of the given languages, from an abstract point of view. First, we introduce the formal semantics of the model modifiers, afterwards we introduce a notion of bisimulation. Bisimulations are an important tool to investigate the expressive power of the languages introduced in this thesis. We show that all the languages are incomparable among them in terms of expressive power (except for the two versions of swap, which we conjecture are also incomparable). We continue by investigating the computational behaviour of this kind of operators. First, we prove that the satisfiability problem for some of the relation-changing modal logics we investigate is undecidable. Then, we prove that the model checking problem is PSpace-complete for the six logics. Finally, we investigate model checking fixing the model and fixing the formula (problems known as formula and program complexity, respectively). We show that it is possible to define complete but non-terminating methods to check satisfiability. We introduce tableau methods for relation-changing modal logics and we prove that all these methods are sound and complete, and we show some applications. In the last part of the thesis, we discuss a concrete context in which we can apply relation-changing modal logics: Dynamic Epistemic Logics (DEL). We motivate the use of the kind of logics that we investigate in this new framework, and we introduce some examples of DEL. Finally, we define a new relation-changing modal logic that embeds DEL and we investigate its computational behaviour.Fil: Fervari, Raúl Alberto. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física; Argentina

Seeing, Knowing, doing : case studies in modal logic

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