This paper studies intentional action in stit logic. The formal logic study of intentional action appears to be new, since most logical studies of intention concern intention as a static mental state. In the formalization we distinguish three modes of acting: the objective level concerning the choices an agent objectively exercises, the subjective level concerning the choices an agent knows or believes to be exercising, and finally, the intentional level concerning the choices an agent intentionally exercises. Several axioms constraining the (...) relations between these different modes of acting will be considered and discussed. The side effect problem will be analyzed as an interaction between knowingly doing and intentionally doing. Non-successful action will be analyzed as a weakening of the epistemic attitude towards action. Finally, the notion of ‘attempt’ will be briefly considered as a further weakening in this direction. (shrink)

The difficulty of defining rational behavior in game situations is that the players'' strategies will depend on their expectations about other players'' strategies. These expectations are beliefs the players come to the game with. Game theorists assume these beliefs to be rational in the very special sense of beingobjectively correct but no explanation is offered of the mechanism generating this property of the belief system. In many interesting cases, however, such a rationality requirement is not enough to guarantee that an (...) equilibrium will be attained. In particular, I analyze the case of multiple equilibria, since in this case there exists a whole set of rational beliefs, so that no player can ever be certain that the others believe he has certain beliefs. In this case it becomes necessary to explicitly model the process of belief formation. This model attributes to the players a theory of counterfactuals which they use in restricting the set of possible equilibria. If it were possible to attribute to the players the same theory of counterfactuals, then the players'' beliefs would eventually converge. (shrink)

We develop a multi-agent deontic action logic to study the logical behaviour of two types of deontic conditionals: (1) conditional obligations, having the form "If group H were to perform action aH, then, in group F's interest, group G ought to perform action aG" and (2) conditional permissions, having the form "If group H were to perform action aH, then, in group F's interest, group G may perform action aG". First, we define a formal language for multi-agent deontic action logic (...) and a class of consequentialist models to interpret the formulas of the language. Second, we define a transformation that converts any strategic game into a consequentialist model. Third, we show that an outcome a* is a Nash equilibrium of a strategic game if and only if a conjunction of certain conditional permissions is true in the consequentialist model that results from the transformation of that strategic game. (shrink)

The aim of this paper, is to provide a logical framework for reasoning about actions, agency, and powers of agents and coalitions in game-like multi-agent systems. First we define our basic Dynamic Logic of Agency ( ). Differently from other logics of individual and coalitional capability such as Alternating-time Temporal Logic (ATL) and Coalition Logic, in cooperation modalities for expressing powers of agents and coalitions are not primitive, but are defined from more basic dynamic logic operators of action and (historic) (...) necessity. We show that STIT logic can be reconstructed in . We then extend with epistemic operators, which allows us to distinguish capability and power. We finally characterize the conditions under which agents are aware of their capabilities and powers. (shrink)

We propose a theory of events and causes against the background of branching time. Notions discussed include possibility based on reality, transitions, events, determinacy, contingency, causes and effects. The main idea in defining causal relations is to introduce a certain preconditioning circumstance under which one event follows another. We also briefly compare this theory with some other theories.

We present a simple theory of actions against the background of branching time, based on which we propose two versions of an extended stit theory, one equipped with particular actions and the other with sets of such actions. After reporting some basic results of a formal development of such a theory, we briefly explore its connection to a version of branching ETL.

The theory of rational decision has always been implicitly involved with subjunctive and counterfactual conditionals. “If I were to do A, this would happen; if I were to do B that would happen. ” When I have done A, I use the counterfactual: “If I had done B, the outcome would have been worse. ” Counterfactuals are handled so smoothly in decision theory and game theory that they are hardly ever explicitly discussed except in cases where they cause problems. For (...) many philosophers, Newcomb’s paradox was such a critical case ). In game theory, questions about beliefs off the equilibrium path in extensive form games and related issues of backward and forward induction provoked explicit discussion of counterfactuals , Bicchieri , Binmore , Harsanyi and Selten , Reny , Stalnaker , ). Where subjunctive conditionals cause problems, we need an explicit theory. What theory should we use? There is the selection function semantics of Stalnaker based on the idea of “most similar possible world in which the antecedent is true”, and related theories of Woodruff , Lewis , Pollock , Nute , which relax some of Stalnaker’s assumptions. (shrink)

Deliberation about what to do in any context requires reasoning about what will or would happen in various alternative situations, including situations that the agent knows will never in fact be realized. In contexts that involve two or more agents who have to take account of each others' deliberation, the counterfactual reasoning may become quite complex. When I deliberate, I have to consider not only what the causal effects would be of alternative choices that I might make, but also what (...) other agents might believe about the potential effects of my choices, and how their alternative possible actions might affect my beliefs. Counterfactual possibilities are implicit in the models that game theorists and decision theorists have developed – in the alternative branches in the trees that model extensive form games and the different cells of the matrices of strategic form representations – but much of the reasoning about those possibilities remains in the informal commentary on and motivation for the models developed. Puzzlement is sometimes expressed by game theorists about the relevance of what happens in a game ‘off the equilibrium path’: of what would happen if what is both true and known by the players to be true were instead false. (shrink)

We show that truth conditions for counterfactuals need not always be given in terms of a vague notion of similarity. To this end, we single out the important class of historical counterfactuals and give formally rigorous truth conditions for these counterfactuals, employing a partial ordering relation called "comparative closeness" that is defined in the framework of branching space-times. Among other applications, we provide a detailed analysis of counterfactuals uttered in the context of lost bets. In an appendix we compare our (...) theory with the branching space-times based reading of counterfactuals recently proposed by Belnap. (shrink)

In this paper we propose a method for modeling social influence within the STIT approach to action. Our proposal consists in extending the STIT language with special operators that allow us to represent the consequences of an agent’s choices over the rational choices of another agent.

We introduce a “reason-based” framework for explaining and predicting individual choices. It captures the idea that a decision-maker focuses on some but not all properties of the options and chooses an option whose motivationally salient properties he/she most prefers. Reason-based explanations allow us to distinguish between two kinds of context-dependent choice: the motivationally salient properties may (i) vary across choice contexts, and (ii) include not only “intrinsic” properties of the options, but also “context-related” properties. Our framework can accommodate boundedly rational (...) and sophisticatedly rational choice. Since properties can be recombined in new ways, it also offers resources for predicting choices in unobserved contexts. (shrink)

Two groups of agents, G1 and G2, face a *moral conflict* if G1 has a moral obligation and G2 has a moral obligation, such that these obligations cannot both be fulfilled. We study moral conflicts using a multi-agent deontic logic devised to represent reasoning about sentences like "In the interest of group F of agents, group G of agents ought to see to it that phi". We provide a formal language and a consequentialist semantics. An illustration of our semantics with (...) an analysis of the Prisoner’s Dilemma follows. Next, necessary and sufficient conditions are given for (1) the possibility that a single group of agents faces a moral conflict, for (2) the possibility that two groups of agents face a moral conflict within a single moral code, and for (3) the possibility that two groups of agents face a moral conflict. (shrink)

John Horty effectively develops deontic logic (the logic of ethical concepts like obligation and permission) against the background of a formal theory of agency. He incorporates certain elements of decision theory to set out a new deontic account of what agents ought to do under various conditions over extended periods of time. Offering a conceptual rather than technical emphasis, Horty's framework allows a number of recent issues from moral theory to be set out clearly and discussed from a uniform point (...) of view. (shrink)

In this volume, John Horty brings to bear his work in logic to present a framework that allows for answers to key questions about reasons and reasoning, namely: What are reasons, and how do they support actions or conclusions?

Written by one of the preeminent researchers in the field, this book provides a comprehensive exposition of modern analysis of causation. It shows how causality has grown from a nebulous concept into a mathematical theory with significant applications in the fields of statistics, artificial intelligence, economics, philosophy, cognitive science, and the health and social sciences. Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections (...) and statistical associations. Cited in more than 2,100 scientific publications, it continues to liberate scientists from the traditional molds of statistical thinking. In this revised edition, Judea Pearl elucidates thorny issues, answers readers' questions, and offers a panoramic view of recent advances in this field of research. Causality will be of interest to students and professionals in a wide variety of fields. Dr Judea Pearl has received the 2011 Rumelhart Prize for his leading research in Artificial Intelligence and systems from The Cognitive Science Society. (shrink)

When evaluating the rationality of a player in a game one has to examine counterfactuals such as "what would happen if the player were to do what he does not do?" In this paper I develop a model of a normal form game where counterfactuals of this sort are evaluated as in the philosophical literature (cf. Lewis, 1973; Stalnaker, 1968). According to this method one evaluates a statement like ``what would the player believe if he were to do what he (...) does not do'' at the world that is closest to the actual world where the hypothetical deviation occurs. I show that in this model common knowledge of rationality need not lead to rationalizability. I also present assumptions that allow rationalizability to follow from common knowledge of rationality. These assumptions suggest that rationalizability may not rely on weaker assumptions about belief consistency than Nash equilibrium. (shrink)

We propose a refinement of STIT logic to make it suitable to model causal agency and responsibility in basic multi-agent scenarios in which agents can interfere with one another. We do this by supplementing STIT semantics, first, with action types and, second, with a relation of opposing between action types. We exploit these novel elements to represent a test for potential causation, based on an intuitive notion of expected result of an action, and two tests for actual causation from the (...) legal literature, i.e. the but-for and the NESS tests. We then introduce three new STIT operators modeling corresponding notions of causal responsibility, which we call potential, strong, and plain responsibility, and use them to provide a fine-grained analysis of a number of case studies involving both individual agents and groups. (shrink)

The goal of this paper is to frame a theory of reasons--what they are, how they support actions or conclusions--using the tools of default logic. After sketching the basic account of reasons as provided by defaults, I show how it can be elaborated to deal with two more complicated issues: first, situations in which the priority relation among defaults, and so reasons as well, is itself established through default reasoning; second, the treatment of undercutting defeat and exclusionary reasons. Finally, and (...) by way of application, I show how the resulting account can shed some light on Jonathan Dancy's argument from reason holism to a form of extreme particularism in moral theory. (shrink)