The aggregation of individual judgments on logically interconnected propositions into a collective decision on the same propositions is called judgment aggregation. Literature in social choice and political theory has claimed that judgment aggregation raises serious concerns. For example, consider a set of premises and a conclusion where the latter is logically equivalent to the former. When majority voting is applied to some propositions (the premises) it may give a different outcome than majority voting applied to another set of propositions (the (...) conclusion). This problem is known as the discursive dilemma (or paradox). The discursive dilemma is a serious problem since it is not clear whether a collective outcome exists in these cases, and if it does, what it is like. Moreover, the two suggested escape-routes from the paradox—the so-called premise-based procedure and the conclusion-based procedure—are not, as I will show, satisfactory methods for group decision-making. In this paper I introduce a new aggregation procedure inspired by an operator defined in artificial intelligence in order to merge belief bases. The result is that we do not need to worry about paradoxical outcomes, since these arise only when inconsistent collective judgments are not ruled out from the set of possible solutions. (shrink)

The aggregation of consistent individual judgments on logically interconnected propositions into a collective judgment on the same propositions has recently drawn much attention. Seemingly reasonable aggregation procedures, such as propositionwise majority voting, cannot ensure an equally consistent collective conclusion. The literature on judgment aggregation refers to such a problem as the \textit{discursive dilemma}. In this paper we assume that the decision which the group is trying to reach is factually right or wrong. Hence, we address the question of how good (...) the various approaches are at selecting the right conclusion. We focus on two approaches: distance-based procedures and a Bayesian analysis. They correspond to group-internal and group-external decision-making, respectively. We compare those methods in a probabilistic model, demonstrate the robustness of our results over various generalizations and discuss their applicability in different situations. The findings vindicate (i) that in judgment aggregation problems, reasons should carry higher weight than conclusions and (ii) that considering members of an advisory board to be highly competent is a better strategy than to underestimate their advice.". (shrink)

The paper discusses ten philosophical problems in deontic logic: how to formally represent norms, when a set of norms may be termed ‘coherent’, how to deal with normative conflicts, how contraryto-duty obligations can be appropriately modeled, how dyadic deontic operators may be redefined to relate to sets of norms instead of preference relations between possible worlds, how various concepts of permission can be accommodated, how meaning postulates and counts-as conditionals can be taken into account, and how sets of norms may (...) be revised and merged. The problems are discussed from the viewpoint of input/output logic as developed by van der Torre & Makinson. We argue that norms, not ideality, should take the central position in deontic semantics, and that a semantics that represents norms, as input/output logic does, provides helpful tools for analyzing, clarifying and solving the problems of deontic logic. (shrink)

The Ostrogorski paradox and the discursive dilemma are seemingly unrelated paradoxes of aggregation. The former is discussed in traditional social choice theory, while the latter is at the core of the new literature on judgment aggregation. Both paradoxes arise when, in a group, each individual consistently makes a judgment, or expresses a preference, (in the form of yes or no) over specific propositions, and the collective outcome is in some respect inconsistent. While the result is logically inconsistent in the case (...) of the discursive paradox, it is not stable with respect to the level of aggregation in the case of the Ostrogorski paradox. In the following I argue that, despite these differences, the two problems have a similar structure. My conclusion will be twofold: on the one hand, the similarities between the paradoxes support the claim that these problems should be tackled using the same aggregation procedure; on the other hand, applying the same procedure to these paradoxes will help clarify the strengths and weaknesses of the aggregation method itself. More specifically, I will show that an operator defined in artificial intelligence to merge belief bases can deal with both paradoxes. (shrink)

This paper provides algorithmic options for belief revision of a database receiving an infinite stream of inputs. At stage , the database is ¡£¢ , receiving the input ¤ ¢ . The revision algorithms for moving to the new database ¡ ¢¦¥¨§© ¡ ¢ ¤ ¢ take into account the history of previous revisions actually executed as well as possible revision options which were discarded at the time but may now be pursued. The appropriate methodology for carrying this out is (...) Labelled Deductive Systems. (shrink)

Judgment aggregation studies how individual opinions on a given set of propositions can be aggregated to form a consistent group judgment on the same propositions. Despite the simplicity of the problem, seemingly natural aggregation procedures fail to return consistent collective outcomes, leading to what is now known as the doctrinal paradox. The first occurrences of the paradox were discovered in the legal realm. However, the interest of judgment aggregation is much broader and extends to political philosophy, epistemology, social choice theory, (...) and computer science. The aim of this paper is to provide a concise survey of the discipline and to outline some of the most pressing questions and future lines of research. (shrink)

One of the major problems that artificial intelligence needs to tackle is the combination of different and potentially conflicting sources of information. Examples are multi-sensor fusion, database integration and expert systems development. In this paper we are interested in the aggregation of propositional logic-based information, a problem recently addressed in the literature on information fusion. It has applications in multi-agent systems that aim at aggregating the distributed agent-based knowledge into an (ideally) unique set of propositions. We consider a group of (...) autonomous agents who individually hold a logically consistent set of propositions. Each set of propositions represents an agent’s beliefs on issues on which the group has to make a collective decision. To make the collective decision, several aggregation procedures have been proposed in the literature. Assuming that all propositions in question are factually right or wrong, we ask how good belief fusion is as a truth tracker. Will it single out the true set of propositions? And how does information fusion compare with other aggregation procedures? We address these questions in a probabilistic framework and show that information fusion does especially well for agents with a middling competence of hitting the truth of an individual proposition. (shrink)

The problem of the aggregation of consistent individual judgments on logically interconnected propositions into a collective judgment on the same propositions has recently drawn much attention. The dificulty lies in the fact that a seemingly reasonable aggregation procedure, such as propositionwise majority voting, cannot ensure an equally consistent collective outcome. The literature on judgment aggregation refers to such dilemmas as the discursive paradox. So far, three procedures have been proposed to overcome the paradox: the premise-based and conclusion-based procedures on the (...) one hand, and the merging approach on the other hand. In this paper we assume that the decision which the group is trying to reach is factually right or wrong. Hence, the question is how good the merging approach is in tracking the truth, and how it compares with the premise-based and conclusion-based procedures. (shrink)

ment on the same propositions, and is plagued by impossibility re- 2. What is the role of independence in judgment aggregation sults. In this paper we study the central notion of independence in..

Formal arguments are often represented by pairs, but in this paper we consider normative arguments represented by sequences of triples, where constitutive norms derive institutional facts from brute facts, and regulative norms derive deontic facts like obligations and permissions from institutional facts. The institutional facts may be seen as the reasons explaining or warranting the deontic obligations and permissions, and therefore they can be attacked by other normative arguments too. We represent different aspects of normative reasoning by different kinds of (...) consistency checks among these triples, and we use formal argumentation theory to resolve conflicts among such normative arguments. In particular, we introduce various requirements for arguing about norms concerning violations, contrary-to-duty obligations, dilemmas, conflict resolution and different kinds of norms, and we introduce a formal argumentation theory satisfying the requirements. In order to illustrate our framework, we introduce a running example based on university regulations for prospective and actual students. (shrink)

The combination of individual judgments on logically interconnected propositions into a collective decision on the same propositions is called judgment aggregation. Literature in social choice and political theory has claimed that judgment aggregation raises serious concerns. For example, consider a set of premises and a conclusion in which the latter is logically equivalent to the former. When majority voting is applied to some propositions (the premises) it may give a different outcome than majority voting applied to another set of propositions (...) (the conclusion). This problem is known as the doctrinal paradox. The doctrinal paradox is a serious problem since it is not clear whether a collective outcome exists in these cases, and if it does, what it is like. Moreover, the two suggested escape-routes from the paradox - the so-called premise-based procedure and the conclusion-based procedure - are not, as I will show, satisfactory methods for group decision-making. In this paper I introduce a new aggregation procedure inspired by an operator defined in artificial intelligence in order to merge knowledge bases. The result is that we do not need to worry about paradoxical outcomes, since these arise only when inconsistent collective judgments are not ruled out from the set of possible solutions. (shrink)

In this paper we consider the relation between beliefs and goals in agent theory. Beliefs play three roles in reasoning about goals: they play a role in the generation of unconditional desires from conditional ones, they play a role in adoption of desires as goals, and they play a role in the selection of plans to achieve goals. In this paper we consider the role of goals in reasoning about beliefs. Though we assume that goals do not play a role (...) in the belief generation problem, we argue that they play a role in the belief selection problem. We show the rationality of the use of goals in belief selection, in the sense that there are cases in which agents that take their goals into account in selecting a belief set from a set of alternatives outperform agents that do not do so. We also formally distinguish between the rational role of goals in belief selection and irrational wishful thinking. (shrink)

In this paper we explore the relation between three areas: judgment aggregation, belief merging and social choice theory. Judgment aggregation studies how to aggregate individual judgments on logically interconnected propositions into a collective decision on the same propositions. When majority voting is applied to some propositions it may however give a different outcome than majority voting applied to another set of propositions. Starting from this so-called doctrinal paradox, the paper surveys the literature on judgment aggregation, and shows that the application (...) of a well known belief merging operator can dissolve the paradox. Finally, the use of distances is shown to establish a link between belief merging and preference aggregation in social choice theory. (shrink)

In this paper we study AGM contraction and revision of rules using input/output logical theories. We replace propositional formulas in the AGM framework of theory change by pairs of propositional formulas, representing the rule based character of theories, and we replace the classical consequence operator Cn by an input/output logic. The results in this paper suggest that, in general, results from belief base dynamics can be transferred to rule base dynamics, but that a similar transfer of AGM theory change to (...) rule change is much more problematic. First, we generalise belief base contraction to rule base contraction, and show that two representation results of Hansson still hold for rule base contraction. Second, we show that the six so-called basic postulates of AGM contraction are consistent only for some input/output logics, but not for others. In particular, we show that the notorious recovery postulate can be satisfied only by basic output, but not by simple-minded output. Third, we show how AGM rule revision can be defined in terms of AGM rule contraction using the Levi identity. We highlight various topics for further research. (shrink)

This paper presents and discusses a novel approach to indeterministic belief revision. An indeterministic belief revision operator assumes that, when an agent is confronted with a new piece of information, it can revise its belief sets in more than one way. We define a rational agent not only in terms of what it believes but also of what it desires and wants to achieve. Hence, we propose that the agent’s goals play a role in the choice of (possibly) one of (...) the several available revision options. Properties of the new belief revision mechanism are also investigated. (shrink)

Lewis’ Principal Principle (PP) aims at clarifying the connection between chance (i.e. objective probability) and credence (i.e. subjective probability). It is generally assumed that the chance that an event will occur does not depend on our credence in the occurrence of that event. Nevertheless, chances constrain our credence, and Lewis’ PP is an attempt to capture this connection.

The problem of the aggregation of inputs coming from different sources arises in several contexts. Examples are the combination of individual preferences (studied in social choice theory), opinions (judgment aggregation), and data (artificial intelligence). While a number of results are available in each of these disciplines, a question that has been addressed only recently is how similar these aggregation problems are, despite the different types of inputs they try to combine.