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ICR - Individual and Collective Reasoning

Researchers

Overview

Aim of the project is to investigate aspects of individual and collective rationality and to develop formal approaches for their representation. In particular, we are interested both in the generalization of existing frameworks for individual agent reasoning to its collective counterpart, and in the study and representation of the interactions between agents in a group.

Subprojects

  1. Feasible Procedures for Judgment Aggregation (Gabriella Pigozzi)
  2. Collective Reasoning Procedures for Knowledge-Based Agents (Judgment Aggregation for Computer Science) (Gabriella Pigozzi, Marija Slavkovik and Leon van der Torre)
  3. Normative Framework for Normative System Change (Gabriella Pigozzi and Leon van der Torre)
  4. Logics for Artificial Normative Systems Design (Davide Grossi)
  5. Semantics for Logic Programming and Solution Concepts in Games (Patrizio Barbini, Davide Grossi, and Filiz Uygun)

1. Feasible Procedures for Collective-Decision Making

Judgment aggregation is an emerging research area in economics that studies how individual opinions on logically interconnected propositions can be mapped into a collective judgment on the same propositions [List 2007]. Examples are the aggregations of agents’ judgments in expert panels, legal courts, boards, and councils. This discipline has recently attracted attention in multi-agent systems and artificial intelligence, for example for the combination of opinions of equally reliable agents. Unfortunately, most of the work in judgment aggregation focuses on impossibility results. In this project we explore feasible procedures for group decisions. This is achieved along two directions:

  1. Theoretical investigation of the connections between logical theories of revision and group decisions.
  2. Proposals of more realistic framework than those introduced in the literature in order to provide possibility results to the problem of judgment aggregation.)

There is a strong connection between logical theories of revision and collective decision-making. They both share the common mechanism of trying to resolve conflicting alternatives. While the logical theories of revision investigate the several ways a theory can be revised, individual decision making studies how an individual should choose among incompatible courses of actions, and the theory of voting tries to reconcile competing voters. In all these cases a resolution is required. The formal relations between logical models for belief change and the theory of voting has been studied in [Gabbay et al. 2007].

More specifically, the relations between belief fusion and judgment aggregation have been clarified in [Pigozzi 2006]. Here, it was shown that procedures defined in belief fusion can be fruitfully imported into collective decision-making and used to resolve various paradoxes arising in judgment aggregation and in social choice theory (such as the Ostrogorski paradox) [Pigozzi 2005]. Moreover, in order to evaluate the truth-tracking properties of the fusion procedure, a probabilistic model has been investigated in [Pigozzi and Hartmann 2007].

Finally, a more realistic framework for judgment aggregation has been proposed in [Benamara et al. 2008]. Here, standard judgment aggregation approach has been extended by taking into account the confidence a group member has in the decision rule. This is achieved by allowing the individuals to assign weights to the criteria that are relevant for the final decision. The confidence score in the rule is computed on the basis of such weights, and it expresses how well-suited a group member thinks that the adopted rule is for the decision process. This new representation leads to avoid most cases of indecision by using specific decision rule (conclusion-based or premises-based) according to the value of the confidence score.

2. Collective Reasoning Procedures for Knowledge-Based Agents (Judgment Aggregation for Computer Science)

To address the problem of collective reasoning for artificial agents, a suitable existing framework has to be either adopted/adapted or developed. The starting point of this research is to consider judgment aggregation as a collective reasoning framework for artificial agents. However, existing approaches to judgment aggregation do not allow for group members to reason together (by communication, for example) after submitting their initial opinions. Furthermore, the field of judgment aggregation is still not mature enough to offer satisfactory solution methodologies for group reasoning.

Judgment aggregation is relatively a new field of research. It has been primarily focusing on determining the minimum set of rationality axioms under which aggregation procedures are possible. With due exceptions, to these days it is plagued with impossibility results. In [Pigozzi and van der Torre 2007, Pigozzi et al. 2008] the independence condition used in judgment aggregation has been criticized and, consequently, new independence assumptions that distinguish premises from conclusion are introduced. By introducing new operators that satisfy the new independence assumptions, the problematic impossibility results no longer hold.

Goal of this research is to develop a new approach that avoids the pitfalls of judgment aggregation (i.e. allows for rational aggregation procedures to be possible) and such that can be used as a reasoning framework for knowledge-based agents.

3. Normative Framework for Normative System Change

It is often observed that in a multi-agent system, normative systems must be able to evolve over time. For example, normative system change may be due to actions of agents that create or remove norms in the system. However, less has been said about how normative systems should change [Hansen et al. 2007]. Also, there is no formal framework to evaluate normative system change methods, and there is no formal classification of normative system change.

Belief revision studies how a set of propositions should change in view of a possibly new conflicting information. The most well known belief revision theory is AGM, which provides a set of postulates that the new belief set should satisfy. However, typically there are several sets that satisfy the conditions and no solution about which one to chose is provided.

Belief revision respects a number of postulates which are useful in the setting of norm change, like success, the retracted proposition should not be obligatory anymore, or minimality. Also work on belief change suggests that there are many approaches, since belief change is concerned with sets of propositions only, and in norm change we have sets of pairs of propositions (and belief change is a special case of norm change). This leads to our central research question: How should we evaluate and classify norm change methods? This breaks down into the following questions:

  1. Which abstract model of normative system change?.
  2. How to classify norm contraction methods?
  3. How to classify norm revision methods?

In [Boella et al. 2008] we show that if we replace propositional formulas by pairs of propositional formulas, representing the rule based character of norms, then some of the properties cannot be expressed, and other properties are consistent only for some logics, but not for others. We therefore introduce a new formal framework for norm change, and we study contraction and revision of norms in this framework.

4. Logics for Artificial Normative Systems Design

Designing a normative system does not only mean to state a number of standards of behavior (e.g., norms, or laws), but also to organize the society in such a way that those standards of behavior can reasonably be met without reducing agents’ autonomy. For instance, in e-commerce systems a typical safe-exchange problem arises. In that context norms such as “sellers ought to ship the purchased good immediately after receiving payment” are issued aiming at increasing trust between the interacting parties. In addition, a mechanism that creates the necessary incentives for sellers to comply with the norm (e.g., a reputation system by means of which purchaser could retaliate non-abiding sellers) is needed in the system. If no such mechanism is put into place the norm is just likely not to be complied with. This simple example represents an ubiquitous pattern in human normative systems which, once properly addressed in its general form and with formal tools, could be incorporated in artificial normative systems as well.

The expected result of the project consists in the development of a logic (or of a family of logics) which can be used for the formal representation and analysis of normative systems and their implementations. Such formalisms will provide solid foundations for the design of artificial normative systems (for instance in the e-commerce and e-governments domains) in that they will provide formal languages for talking and reasoning about properties of mechanisms w.r.t. formally specified normative systems.

An essential step towards the understanding of the norm implementation issue has been made in [Grossi 2008], where the notion of social choice function has been investigated by logical means. Such notion lies at the core of the mechanism design and implementation theories, that is, of the game-theoretic disciplines whose results the project intends to import in the context of normative systems. The possibility of analyzing social choice functions from a logic-based point of view paves the way for a logic-based understanding of norm implementation. The norm implementation issue itself has been given a preliminary account in [Grossi et al. 2008], where a number of norm-enforcement methods are formalized by making use of labeled transition systems, which constitute the basic formal semantic machinery the project intends to exploit.

5. Semantics for Logic Programming and Solution Concepts in Games

The project addresses the relations between Logic Programming, and in particular Answer Set Programming, and Game Theory. Some results on this issue are already available in the literature. They concern, more specifically, the way the stable semantics for Logic Programming is related to the solution concept of Nash Equilibrium in n-persons games. First objective of the project is to provide a comprehensive literature overview and a classification of the results available on the issue at this moment. On the literature overview will be based the second objective of the project. This will consist in identifying, under our supervision, one feasible research direction on the issue, and in advancing a new concrete contribution.

References

icr.uni.lu —