Gabriella Pigozzi

Normative framework for normative system change

The paper proposes a complex adaptive systems approach to the formation of an ontology and a shared lexicon in a group of distributed agents with only local interactions and no central control authority. The underlying mechanisms are explained in some detail and results of some experiments with robotic agents are briefly reported.Normative systems in a multiagent system must be able to evolve over time, for example due to actions creating or removing norms in the system. The only formal framework to evaluate and classify normative system change methods is the so-called AGM framework of theory change, which has originally been developed as a framework to describe and classify both belief and normative system change. However, it has been used for belief change only, since the beliefs or norms are represented as propositional formulas. We therefore propose, as a normative framework for normative system change, to replace propositional formulas in the AGM framework of theory change by pairs of propositional formulas, representing the rule based character of norms, and to add several principles from the input/output logic framework. In this new framework, we show that some of the AGM properties cannot be expressed, and other properties are consistent only for some logics, but not for others.

Belief merging and the discursive dilemma: an argument-based account to paradoxes of judgment aggregation

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.

On judgment aggregation in abstract argumentation

Judgment aggregation is a field in which individuals are required to vote for or against a certain decision (the conclusion) while providing reasons for their choice. The reasons and the conclusion are logically connected propositions. The problem is how a collective judgment on logically interconnected propositions can be defined from individual judgments on the same propositions. It turns out that, despite the fact that the individuals are logically consistent, the aggregation of their judgments may lead to an inconsistent group outcome, where the reasons do not support the conclusion. However, in this paper we claim that collective irrationality should not be the only worry of judgment aggregation. For example, judgment aggregation would not reject a consistent combination of reasons and conclusion that no member voted for. In our view this may not be a desirable solution. This motivates our research about when a social outcome is ‘compatible’ with the individuals’ judgments. The key notion that we want to capture is that any individual member has to be able to defend the collective decision. This is guaranteed when the group outcome is compatible with its members views. Judgment aggregation problems are usually studied using classical propositional logic. However, for our analysis we use an argumentation approach to judgment aggregation problems. Indeed the question of how individual evaluations can be combined into a collective one can also be addressed in abstract argumentation. We introduce three aggregation operators that satisfy the condition above, and we offer two definitions of compatibility. Not only does our proposal satisfy a good number of standard judgment aggregation postulates, but it also avoids the problem of individual members of a group having to become committed to a group judgment that is in conflict with their own individual positions.

Judgment aggregation rules based on minimization

Many voting rules are based on some minimization principle. Likewise, in the field of logic-based knowledge representation and reasoning, many belief change or inconsistency handling operators also make use of minimization. Surprisingly, minimization has not played a major role in the field of judgment aggregation, in spite of its proximity to voting theory and logic-based knowledge representation and reasoning. Here we make a step in this direction and study six judgment aggregation rules; two of them, based on distances, have been previously defined; the other four are new, and all inspired both by voting theory and knowledge representation and reasoning. We study the inclusion relationships between these rules and address some of their social choice theoretic properties.

Judgment Aggregation: A Primer

Judgment aggregation is a mathematical theory of collective decision-making. It concerns the methods whereby individual opinions about logically interconnected issues of interest can, or cannot, be aggregated into one collective stance. Aggregation problems have traditionally been of interest for disciplines like economics and the political sciences, as well as philosophy, where judgment aggregation itself originates from, but have recently captured the attention of disciplines like computer science, artificial intelligence and multi-agent systems. Judgment aggregation has emerged in the last decade as a unifying paradigm for the formalization and understanding of aggregation problems. Still, no comprehensive presentation of the theory is available to date. This Synthesis Lecture aims at filling this gap presenting the key motivations, results, abstractions and techniques underpinning it.

Reliable Methods of Judgement Aggregation

The aggregation of consistent individual judgements on logically interconnected propositions into a collective judgement 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 judgement aggregation refers to such a problem as the discursive dilemma. In this article 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 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 whose assumptions are subsequently relaxed. Our findings have two general implications for judgement aggregation problems: first, in a voting procedure, reasons should carry higher weight than the conclusion, and second, considering members of an advisory board to be highly competent is a better strategy than discounting their advice.

Preferences in artificial intelligence

The paper presents a focused survey about the presence and the use of the concept of “preferences” in Artificial Intelligence. Preferences are a central concept for decision making and have extensively been studied in disciplines such as economy, operational research, decision analysis, psychology and philosophy. However, in the recent years it has also become an important topic both for research and applications in Computer Science and more specifically in Artificial Intelligence, in fields spanning from recommender systems to automatic planning, from non monotonic reasoning to computational social choice and algorithmic decision theory. The survey essentially covers the basics of preference modelling, the use of preference in reasoning and argumentation, the problem of compact representations of preferences, preference learning and the use of non conventional preference models based on extended logical languages. It aims at providing a general reference for all researchers both in Artificial Intelligence and Decision Analysis interested in this exciting interdisciplinary topic.

Manipulation in group argument evaluation

Given an argumentation framework and a group of agents, the individuals may have divergent opinions on the status of the arguments. If the group needs to reach a common position on the argumentation framework, the question is how the individual evaluations can be mapped into a collective one. This problem has been recently investigated in 1]. In this paper, we study under which conditions these operators are Pareto optimal and whether they are manipulable.

A Complete Conclusion-Based Procedure for Judgment Aggregation

Judgment aggregation is a formal theory reasoning about how a group of agents can aggregate individual judgments on connected propositions into a collective judgment on the same propositions. Three procedures for successfully aggregating judgments sets are: premise-based procedure, conclusion-based procedure and distance-based merging. The conclusion-based procedure has been little investigated because it provides a way to aggregate the conclusions, but not the premises, thus it outputs an incomplete judgment set. The goal of this paper is to present a conclusion-based procedure outputting complete judgment sets.

Group intention is social choice with commitment

An agent intends g if it has chosen to pursue goal g an is committed to pursuing g . How do groups decide on a common goal? Social epistemology offers two views on collective attitudes: according to the summative approach, a group has attitude P if all or most of the group members have the attitude P; according to the non-summative approach, for a group to have attitude P it is required that the members together agree that they have attitude P. The summative approach is used extensively in multi-agent systems. We propose a formalization of non-summative group intentions, using social choice to determine the group goals. We use judgment aggregation as a decision-making mechanism and a multi-modal multi-agent logic to represent the collective attitudes, as well as the commitment and revision strategies for the groups intentions.