A Logic for Collective Choice

International audienceThis paper presents a modal logic for modelling individual and collective choices over a set of feasible alternatives. The logic extends propositional logic with a binary modality so that a formula can express not only properties of alternatives but also priorities of individuals over the properties. More importantly, each formula of this logic determines a preference ordering over alternatives based on the priorities over properties that the formula expresses. In such a way, preferences of multiple agents can be represented by a set of formulas in the same logic. This allows us to treat the problem of collective choice in a multi-agent system as aggregation of logical formulas. We further use this language to express a few plausible collective choice rules. Similar to preference aggregation, we specify collective choice rules by Arrow’s conditions. Interestingly, all Arrowian conditions are plausible under the new setting except Independence of Irrelevant Alternatives. This gives us a natural way to avoid Arrow’s impossibility result. Finally, we develop a model checking algorithm to automatically generate individual and collective choices in the logic

Logics for modelling collective attitudes

We introduce a number of logics to reason about collective propositional attitudes that are defined by means of the majority rule. It is well known that majoritarian aggregation is subject to irrationality, as the results in social choice theory and judgment aggregation show. The proposed logics for modelling collective attitudes are based on a substructural propositional logic that allows for circumventing inconsistent outcomes. Individual and collective propositional attitudes, such as beliefs, desires, obligations, are then modelled by means of minimal modalities to ensure a number of basic principles. In this way, a viable consistent modelling of collective attitudes is obtained

The possibility of judgment aggregation for network agendas

Within social choice theory, the new field of judgment aggregation aims at reaching collective judgments on a set of logically interconnected propositions. I investigate decision problems, in which the agenda is a network, composed of atomic propositions and connection rules between them. Networks can represent various realistic decision problems, including most concrete examples given in the literature. Nevertheless, networks are unexplored so far due to problems when modelling connection rules in standard propositional logic. By extending the logic, I prove that, for any network, decision rules satisfying the common conditions always exist, in contrast to the literature's emphasis on impossibilities. I also characterise the class of such decision rules, and propose a simple way to select a decision rule.judgment aggregation, collective inconsistency, possibility theorems, network, connection rule, formal logic, material conditional, subjunctive conditional

A logical analysis of responsibility attribution : emotions, individuals and collectives

International audienceThe aim of this article is to provide a logical analysis of the concept of responsibility attribution; that is, how agents ascribe responsibility about the consequences of actions, either to themselves or to other agents. The article is divided in two parts. The first part investigates the importance of the concept of responsibility attribution for emotion theory in general and, in particular, for the theory of attribution emotions such as guilt, pride, moral approval and moral disapproval. The second part explores the collective dimension of responsibility attribution and attribution emotions, namely the concepts of collective responsibility and collective guilt. The proposed analysis is based on an extension of the logic STIT (the logic of ‘Seeing To It That’) with three different types of knowledge and common knowledge modal operators depending on the time of choice: before one’s choice, after one’s choice but before knowing the choices of other agents, and after the choices of all agents have become public. Decidability of the satisfiability problem of the logic is studied in the article

The Logic of Reciprocity: Trust, Collective Action, and Law

The Logic of Collective Action has for decades supplied the logic of public-policy analysis. In this pioneering application of public choice theory, Mancur Olson elegantly punctured the premise - shared by a variety of political theories - that individuals can be expected to act consistently with the interest of the groups to which they belong. Absent externally imposed incentives, wealth-maximizing individuals, he argued, will rarely find it in their interest to contribute to goods that benefit the group as a whole, but rather will free ride on the contributions that other group members make. As a result, too few individuals will contribute sufficiently, and the well-being of the group will suffer. These assumptions dominate public-policy analysis and public policy itself across a host of regulatory domains - from tax collection to environmental conservation, from street-level policing to policing of the internet. But as a wealth of social science evidence now makes clear, Olson\u27s Logic is false. In collective-action settings, individuals adopt not a materially calculating posture but rather a richer, more emotionally nuanced reciprocal one. When they perceive that others are behaving cooperatively, individuals are moved by honor, altruism, and like dispositions to contribute to public goods even without the inducement of material incentives. When, in contrast, they perceive that others are shirking or otherwise taking advantage of them, individuals are moved by resentment and pride to withhold their own cooperation and even to engage in personally costly forms of retaliation

The Logic of Reciprocity: Trust, Collective Action, and Law

The Logic of Collective Action has for decades supplied the logic of public policy analysis. In this pioneering application of public choice theory, Mancur Olson ele gantly punctured the premise -- shared by a diverse variety of political theories -- that individuals can be expected to act consistently with the interest of the groups to which they belong. Absent externally imposed incentives, wealth-maximizing individuals, he argued, will rarely find it in their interest to contribute to goods that benefit the group as a whole, but rather will free ride on the contributions that other group members make. As a result, too few individuals will contribute sufficiently, and the well-being of the group will suffer. These are the assumptions that dominate public policy analysis and ultimately public policy across a host of regulatory domains -- from tax collection to environmental conservation, from street-level policing to policing of the internet

Logics for strategic reasoning and collective decision-making

Strategic decision-making is ubiquitous in everyday life. The analysis of game strategies has been a research theme in game theory for several decades since von Neumann and Morgenstern. Sophisticated models and analysis tools have been developed with wide applications in Economics, Management Science, Social Science and Computer Science, especially in the field of Artificial Intelligence. However, \much of game theory is about the question whether strategic equilibria exist", as Johan van Benthem, a world-leading logician and game-theorist, points out, \but there are hardly any explicit languages for defining, comparing, or combining strategies". Without such a facility it is challenging for computer scientists to build intelligent agents that are capable of strategic decision-making. In the last twenty years, logical approaches have been proposed to tackle this problem. Pioneering work includes Game Logics, Coalition Logic and Alternating-time Temporal Logic (ATL). These logics either provide facilities for expressing and combining games or offer mechanisms for reasoning about strategic abilities of players. But none of them can solve the problem. The intrinsic difficulty in establishing such a logic is that reasoning about strategies requires combinations of temporal reasoning, counterfactual reasoning, reasoning about actions, preferences and knowledge, as well as reasoning about multi-agent interactions and coalitional abilities. More recently, a few new logical formalisms have been proposed by extending ATL with strategy variables in order to express strategies explicitly. However, most of these logics tend to have high computational complexity, because ATL introduces quantifications over strategies (functions), which leaves little hope of building any tractable inference system based on such a logic. This thesis takes up the challenge by using a bottom-up approach in order to create a balance between expressive power and computational efficiency. Instead of starting with a highly complicated logic, we propose a set of logical frameworks based on a simple and practical logical language, called Game Description Language (GDL), which has been used as an official language for General Game Playing (GGP) since 2005. To represent game strategies, we extend GDL with two binary prioritized connectives for combining actions in terms of their priorities specified by these connectives, and provide it with a semantics based on the standard state transition model. To reason about the strategic abilities of players, we further extend the framework with coalition operators from ATL for specifying the strategic abilities of players. More importantly, a unified semantics is provided for both GDL- and ATL- formulas, which allows us to verify and reason about game strategies. Interestingly, the framework can be used to formalize the fundamental game-playing principles and formally derive two well-known results on two-player games: Weak Determinacy and Zermelo's Theorem. We also show that the model-checking problem of the logic is not worse than that of ATL*, an extension of ATL. To deal with imperfect information games, we extend GDL with the standard epistemic operators and provide it with a semantics based on the epistemic state transition model. The language allows us to specify an imperfect information game and formalize its epistemic properties. Meanwhile, the framework allows us to reason about players' own as well as other players' knowledge during game playing. Most importantly, the logic has a moderate computational complexity, which makes it significantly different from similar existing frameworks. To investigate the interplay between knowledge shared by a group of players and its coalitional abilities, we provide a variant of semantics for ATL with imperfect information. The relation between knowledge sharing and coalitional abilities is investigated through the interplay of epistemic and coalition modalities. Moreover, this semantics is able to preserve the desirable properties of coalitional abilities. To deal with collective decision-making, we apply the approach of combining actions via their priorities for collective choice. We extend propositional logic with the prioritized connective for modelling reason-based individual and collective choices. Not only individual preferences but also aggregation rules can be expressed within this logic. A model-checking algorithm for this logic is thus developed to automatically generate individual and collective choices. In many real-world situations, a group making collective judgments may assign individual members or subgroups different priorities to determine the collective judgment. We design an aggregation rule based on the priorities of individuals so as to investigate how the judgment from each individual affects group judgment in a hierarchical environment. We also show that this rule satisfies a set of plausible conditions and has a tractable computational complexity

Logics for strategic reasoning and collective decision-making

Strategic decision-making is ubiquitous in everyday life. The analysis of game strategies has been a research theme in game theory for several decades since von Neumann and Morgenstern. Sophisticated models and analysis tools have been developed with wide applications in Economics, Management Science, Social Science and Computer Science, especially in the field of Artificial Intelligence. However, \much of game theory is about the question whether strategic equilibria exist", as Johan van Benthem, a world-leading logician and game-theorist, points out, \but there are hardly any explicit languages for defining, comparing, or combining strategies". Without such a facility it is challenging for computer scientists to build intelligent agents that are capable of strategic decision-making. In the last twenty years, logical approaches have been proposed to tackle this problem. Pioneering work includes Game Logics, Coalition Logic and Alternating-time Temporal Logic (ATL). These logics either provide facilities for expressing and combining games or offer mechanisms for reasoning about strategic abilities of players. But none of them can solve the problem. The intrinsic difficulty in establishing such a logic is that reasoning about strategies requires combinations of temporal reasoning, counterfactual reasoning, reasoning about actions, preferences and knowledge, as well as reasoning about multi-agent interactions and coalitional abilities. More recently, a few new logical formalisms have been proposed by extending ATL with strategy variables in order to express strategies explicitly. However, most of these logics tend to have high computational complexity, because ATL introduces quantifications over strategies (functions), which leaves little hope of building any tractable inference system based on such a logic. This thesis takes up the challenge by using a bottom-up approach in order to create a balance between expressive power and computational efficiency. Instead of starting with a highly complicated logic, we propose a set of logical frameworks based on a simple and practical logical language, called Game Description Language (GDL), which has been used as an official language for General Game Playing (GGP) since 2005. To represent game strategies, we extend GDL with two binary prioritized connectives for combining actions in terms of their priorities specified by these connectives, and provide it with a semantics based on the standard state transition model. To reason about the strategic abilities of players, we further extend the framework with coalition operators from ATL for specifying the strategic abilities of players. More importantly, a unified semantics is provided for both GDL- and ATL- formulas, which allows us to verify and reason about game strategies. Interestingly, the framework can be used to formalize the fundamental game-playing principles and formally derive two well-known results on two-player games: Weak Determinacy and Zermelo's Theorem. We also show that the model-checking problem of the logic is not worse than that of ATL*, an extension of ATL. To deal with imperfect information games, we extend GDL with the standard epistemic operators and provide it with a semantics based on the epistemic state transition model. The language allows us to specify an imperfect information game and formalize its epistemic properties. Meanwhile, the framework allows us to reason about players' own as well as other players' knowledge during game playing. Most importantly, the logic has a moderate computational complexity, which makes it significantly different from similar existing frameworks. To investigate the interplay between knowledge shared by a group of players and its coalitional abilities, we provide a variant of semantics for ATL with imperfect information. The relation between knowledge sharing and coalitional abilities is investigated through the interplay of epistemic and coalition modalities. Moreover, this semantics is able to preserve the desirable properties of coalitional abilities. To deal with collective decision-making, we apply the approach of combining actions via their priorities for collective choice. We extend propositional logic with the prioritized connective for modelling reason-based individual and collective choices. Not only individual preferences but also aggregation rules can be expressed within this logic. A model-checking algorithm for this logic is thus developed to automatically generate individual and collective choices. In many real-world situations, a group making collective judgments may assign individual members or subgroups different priorities to determine the collective judgment. We design an aggregation rule based on the priorities of individuals so as to investigate how the judgment from each individual affects group judgment in a hierarchical environment. We also show that this rule satisfies a set of plausible conditions and has a tractable computational complexity

Ontology Merging as Social Choice

The problem of merging several ontologies has important applications in the Semantic Web, medical ontology engineering and other domains where information from several distinct sources needs to be integrated in a coherent manner.We propose to view ontology merging as a problem of social choice, i.e. as a problem of aggregating the input of a set of individuals into an adequate collective decision. That is, we propose to view ontology merging as ontology aggregation. As a first step in this direction, we formulate several desirable properties for ontology aggregators, we identify the incompatibility of some of these properties, and we define and analyse several simple aggregation procedures. Our approach is closely related to work in judgment aggregation, but with the crucial difference that we adopt an open world assumption, by distinguishing between facts not included in an agent’s ontology and facts explicitly negated in an agent’s ontology