Automating Agential Reasoning: Proof-Calculi and Syntactic Decidability for STIT Logics

This work provides proof-search algorithms and automated counter-model extraction for a class of STIT logics. With this, we answer an open problem concerning syntactic decision procedures and cut-free calculi for STIT logics. A new class of cut-free complete labelled sequent calculi G3LdmL^m_n, for multi-agent STIT with at most n-many choices, is introduced. We refine the calculi G3LdmL^m_n through the use of propagation rules and demonstrate the admissibility of their structural rules, resulting in auxiliary calculi Ldm^m_nL. In the single-agent case, we show that the refined calculi Ldm^m_nL derive theorems within a restricted class of (forestlike) sequents, allowing us to provide proof-search algorithms that decide single-agent STIT logics. We prove that the proof-search algorithms are correct and terminate

Logics of knowledge and action: critical analysis and challenges

International audienceWe overview the most prominent logics of knowledge and action that were proposed and studied in the multiagent systems literature. We classify them according to these two dimensions, knowledge and action, and moreover introduce a distinction between individual knowledge and group knowledge, and between a nonstrategic an a strategic interpretation of action operators. For each of the logics in our classification we highlight problematic properties. They indicate weaknesses in the design of these logics and call into question their suitability to represent knowledge and reason about it. This leads to a list of research challenges

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 Logic-Based Analysis of Responsibility

This paper presents a logic-based framework to analyze responsibility, which I refer to as intentional epistemic act-utilitarian stit theory (IEAUST). To be precise, IEAUST is used to model and syntactically characterize various modes of responsibility, where by 'modes of responsibility' I mean instances of Broersen's three categories of responsibility (causal, informational, and motivational responsibility), cast against the background of particular deontic contexts. IEAUST is obtained by integrating a modal language to express the following components of responsibility on stit models: agency, epistemic notions, intentionality, and different senses of obligation. With such a language, I characterize the components of responsibility using particular formulas. Then, adopting a compositional approach -- where complex modalities are built out of more basic ones -- these characterizations of the components are used to formalize the aforementioned modes of responsibility.Comment: In Proceedings TARK 2023, arXiv:2307.0400

Logics of Responsibility

The study of responsibility is a complicated matter. The term is used in different ways in different fields, and it is easy to engage in everyday discussions as to why someone should be considered responsible for something. Typically, the backdrop of these discussions involves social, legal, moral, or philosophical problems. A clear pattern in all these spheres is the intent of issuing standards for when---and to what extent---an agent should be held responsible for a state of affairs. This is where Logic lends a hand. The development of expressive logics---to reason about agents' decisions in situations with moral consequences---involves devising unequivocal representations of components of behavior that are highly relevant to systematic responsibility attribution and to systematic blame-or-praise assignment. To put it plainly, expressive syntactic-and-semantic frameworks help us analyze responsibility-related problems in a methodical way. This thesis builds a formal theory of responsibility. The main tool used toward this aim is modal logic and, more specifically, a class of modal logics of action known as stit theory. The underlying motivation is to provide theoretical foundations for using symbolic techniques in the construction of ethical AI. Thus, this work means a contribution to formal philosophy and symbolic AI. The thesis's methodology consists in the development of stit-theoretic models and languages to explore the interplay between the following components of responsibility: agency, knowledge, beliefs, intentions, and obligations. Said models are integrated into a framework that is rich enough to provide logic-based characterizations for three categories of responsibility: causal, informational, and motivational responsibility. The thesis is structured as follows. Chapter 2 discusses at length stit theory, a logic that formalizes the notion of agency in the world over an indeterministic conception of time known as branching time. The idea is that agents act by constraining possible futures to definite subsets. On the road to formalizing informational responsibility, Chapter 3 extends stit theory with traditional epistemic notions (knowledge and belief). Thus, the chapter formalizes important aspects of agents' reasoning in the choice and performance of actions. In a context of responsibility attribution and excusability, Chapter 4 extends epistemic stit theory with measures of optimality of actions that underlie obligations. In essence, this chapter formalizes the interplay between agents' knowledge and what they ought to do. On the road to formalizing motivational responsibility, Chapter 5 adds intentions and intentional actions to epistemic stit theory and reasons about the interplay between knowledge and intentionality. Finally, Chapter 6 merges the previous chapters' formalisms into a rich logic that is able to express and model different modes of the aforementioned categories of responsibility. Technically, the most important contributions of this thesis lie in the axiomatizations of all the introduced logics. In particular, the proofs of soundness & completeness results involve long, step-by-step procedures that make use of novel techniques

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

Logics for AI and Law: Joint Proceedings of the Third International Workshop on Logics for New-Generation Artificial Intelligence and the International Workshop on Logic, AI and Law, September 8-9 and 11-12, 2023, Hangzhou

This comprehensive volume features the proceedings of the Third International Workshop on Logics for New-Generation Artificial Intelligence and the International Workshop on Logic, AI and Law, held in Hangzhou, China on September 8-9 and 11-12, 2023. The collection offers a diverse range of papers that explore the intersection of logic, artificial intelligence, and law. With contributions from some of the leading experts in the field, this volume provides insights into the latest research and developments in the applications of logic in these areas. It is an essential resource for researchers, practitioners, and students interested in the latest advancements in logic and its applications to artificial intelligence and law

On the computational complexity of ethics: moral tractability for minds and machines

Why should moral philosophers, moral psychologists, and machine ethicists care about computational complexity? Debates on whether artificial intelligence (AI) can or should be used to solve problems in ethical domains have mainly been driven by what AI can or cannot do in terms of human capacities. In this paper, we tackle the problem from the other end by exploring what kind of moral machines are possible based on what computational systems can or cannot do. To do so, we analyze normative ethics through the lens of computational complexity. First, we introduce computational complexity for the uninitiated reader and discuss how the complexity of ethical problems can be framed within Marr’s three levels of analysis. We then study a range of ethical problems based on consequentialism, deontology, and virtue ethics, with the aim of elucidating the complexity associated with the problems themselves (e.g., due to combinatorics, uncertainty, strategic dynamics), the computational methods employed (e.g., probability, logic, learning), and the available resources (e.g., time, knowledge, learning). The results indicate that most problems the normative frameworks pose lead to tractability issues in every category analyzed. Our investigation also provides several insights about the computational nature of normative ethics, including the differences between rule- and outcome-based moral strategies, and the implementation-variance with regard to moral resources. We then discuss the consequences complexity results have for the prospect of moral machines in virtue of the trade-off between optimality and efficiency. Finally, we elucidate how computational complexity can be used to inform both philosophical and cognitive-psychological research on human morality by advancing the moral tractability thesis

The logic of unwitting collective agency

The paper is about the logic of expressions of the form `agent x brings it about that A is the case', or `agent x is responsible for its being the case that A', or `the actions of agent x are the cause of its being the case that A'. Agents could be deliberative (human or computer) agents, purely reactive agents, or simple computational devices. The `brings it about' modalities are intended to express unintentional, perhaps even accidental, consequences of an agent's actions, as well as possibly intentional (intended) ones. Since we make no assumptions at all about the reasoning or perceptual capabilities of the agents we refer to this form of agency as `unwitting'; unwitting can mean both inadvertent and unaware. The semantical framework is a form of labelled transition system extended with an extra component that picks out the actions of a particular agent in a transition, or its `strand' as we call it. We de ne a modal language for talking about the actions of individual agents or groups of agents in transitions, including two de ned modalities of the (unwitting) `brings it about' kind. The novel feature is the switch of attention from talking about an agent's bringing it about that a certain state of a airs exists to talking about an agent's bringing it about that a transition has a certain property. The middle part of the paper presents axiomatisations of the logic, and comments on relationships to other work, in particular on resemblances to P orn's (1977) logic of `brings it about'. The last part is concerned with characterisations of (unwitting) collective agency, that is, the logic of expressions of the form `the set G of agents, collectively though perhaps unwittingly, brings it about that A'