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

A Modal Logic for Explaining some Graph Neural Networks

In this paper, we propose a modal logic in which counting modalities appear in linear inequalities. We show that each formula can be transformed into an equivalent graph neural network (GNN). We also show that each GNN can be transformed into a formula. We show that the satisfiability problem is decidable. We also discuss some variants that are in PSPACE

A Path in the Jungle of Logics for Multi-Agent Systems: on the Relation between General Game-Playing Logics and Seeing-To-It-That Logics

In the recent years, several concurrent logical systems for reasoning about agency and social interaction and for representing game properties have been proposed. The aim of the present paper is to put some order in this 'jungle' of logics by studying the relationship between the dynamic logic of agency DLA and the game description language GDL. The former has been proposed as a variant of the logic of agency STIT by Belnap et al. in which agents' action are named, while the latter has been introduced in AI as a formal language for reasoning about general game-playing. The paper provides complexity results for the satisfiability problems of both DLALogic and GDL as well as a polynomial embedding of GDL into DLA

Big Brother Logic: Logical modeling and reasoning about agents equipped with surveillance cameras in the plane

International audienceWe consider multi-agent scenarios where each agent control sa surveillance camera positioned in the plane, with xed position and angle of view, but rotating freely. The agents can thus observe the surroundings and each other. They can also reason about each other's observation abilities and knowledge derived from these observations. We introduce suitable logical languages for reasoning about such scenarios which involve atomic formulae stating what agents can see, multi-agent epistemic operators for individual, distributed and common knowledge, as well as dynamic operators reflecting the ability of cameras to turn around in order to reach positions satisfying formulae in the language. We introduce semantics of our basic logic BBL and its extensions on natural geometric models, as well as formal Kripke semantics for them in vision-based nite abstractions of the geometric models. We discuss the expressiveness of our logical languages and provide their translations in PDL style. Using these translations we develop algorithms and obtain complexity results for model checking and satisability testing for BBL and its extensions. Notably, we show that even for the extension with common knowledge, model checking remains in PSPACE. Finally, we discuss some further extensions: by adding obstacles, positioning the cameras in 3D or enabling them to change positions

Agents that look at one another

International audienceDespite the fact that epistemic connectives are sometimes interpreted in concrete structures defined by means of runs and clock time functions, one of the things that strikes one when studying multiagent logics is how abstract their semantics are. Contrasting this fact is the fact that real agents like robots in everyday life and virtual characters in video games have strong links with their spatial environment. In this article, we introduce multiagent logics which semantics can be defined by means of purely geometrical notions: possible states are defined by means of the positions in ℝn occupied by agents and the sections of ℝn seen by agents whereas accessibility relations are defined by means of the ability of agents to imagine possible states compatible with what they currently see

Voir, savoir, faire : une étude de cas en logique modale

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.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

Belief merging in Dynamic Logic of Propositional Assignments

International audienceWe study syntactical merging operations that are defined semantically by means of the Hamming distance between valuations; more precisely, we investigate the Σ-semantics, Gmax-semantics and max-semantics. We work with a logical language containing merging operators as connectives, as opposed to the metalanguage operations of the literature. We capture these merging operators as programs of Dynamic Logic of Propositional Assignments DL-PA. This provides a syntactical characterisation of the three semantically defined merging operators, and a proof system for DL-PA therefore also provides a proof system for these merging operators. We explain how PSPACE membership of the model checking and satisfiability problem of star-free DL-PA can be extended to the variant of DL-PA where symbolic disjunctions that are parametrised by sets (that are not defined as abbreviations, but are proper connectives) are built into the language. As our merging operators can be polynomially embedded into this variant of DL-PA, we obtain that both the model checking and the satisfiability problem of a formula containing possibly nested merging operators is in PSPACE