We consider the problem of merging several belief bases in the presence of integrity constraints.

We investigate the logical properties of knowledge base combination operators proposed in the literature. These operators are based on the selection of some maximal subsets of the union of the knowledge bases. We argue that they are not fully satisfactory to merge knowledge bases, since the source of information is lost in the combination process. We show that it is the reason why those operators do not satisfy a lot of logical properties. Then we propose to use more rened selection mechanisms in order to take the distribution of information into account in the combination process. That allows to dene merging operators with a more subtle behaviour. 1 INTRODUCTION In the elds of articial intelligence and databases, one is often faced with conicting information coming from several sources. Thus, an important problem in such cases is how to reach a coherent piece of information from these contradictory ones. For example, if one wants to build an expert system from a ...

An intelligent agent may receive information about its environment from several different sources. How should the agent merge these items of information into a single, consistent piece? Taking our lead from the contraction + expansion approach to belief revision, we envisage a two-stage approach to this problem. The first stage consists of weakening the individual pieces of information into a form in which they can be consistently added together. The second, trivial, stage then consists of simply adding together the information thus obtained. This paper is devoted mainly to the first stage of this process, which we call social contraction. We consider both a postulational and a procedural approach to social contraction. The latter builds on the authorÕs framework of belief negotiation models. With the help of Spohn-type rankings we provide two possible instantiations of this extended framework. This leads to two interesting concrete families of social contraction functions. Ó 2005 Elsevier B.V. All rights reserved.

The importance of belief merging is reflected by the abundance of the literature about it for the last years. In the following, a model for belief merging based on distances is introduced; many merging operators already pointed out so far can be recovered as specific instances of this model. We investigate the computational aspects of such distance-based operators and give two general results showing that the complexity of inference for them is at the first level of the polynomial hierarchy (under very weak assumptions). Then some specific distance-based operators are considered and their complexity is identified. Finally, distancebased merging operators are investigated from the logical point of view.

In this paper, two families of merging operators are considered: quota operators and Gmin operators. Quota operators rely on a simple idea: any possible world is viewed as a model of the result of the merging when it satisfies “sufficiently many” bases from the given profile (a multi-set of bases). Different interpretations of the “sufficiently many” give rise to specific operators. Each Gmin operator is parameterized by a pseudo-distance and each of them is intended to refine the quota operators (i.e., to preserve more information). Quota and Gmin operators are evaluated and compared along four dimensions: rationality, computational complexity, strategy-proofness, and discriminating power. Those two families are shown as interesting alternatives to the formula-based merging operators (which selects some formulas in the union of the bases). 1

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. ∗The title of this paper in an earlier version was “Collective decision-making without paradoxes:

Merging operators aim at defining the beliefs/goals of a group of agents from the beliefs/goals of each member of the group. Whenever an agent of the group has preferences over the possible results of the merging process (i.e. the possible merged bases), she can try to rig the merging process by lying on her true beliefs/goals if this leads to a better merged base according to her point of view. Obviously, strategy-proof operators are highly desirable in order to guarantee a fair merging process even when some of them are not sincere. In fact, when strategy-proofness is not guaranteed, it may be questioned whether the result of the merging process actually represents the beliefs/goals of the group. In this paper, the strategy-proof landscape for many merging operators from the literature, including model-based ones and formula-based ones, is drawn. Both the general case and several restrictions on the merging process (among others, the number of agents and the presence of integrity constraints), are considered.

ABSTRACT. We propose in this paper a new family of belief merging operators, that is based on a game between sources: until a coherent set of sources is reached, at each round a contest is organized to find out the weakest sources, then those sources has to concede (weaken their point of view). This idea leads to numerous new interesting operators (depending of the exact meaning of “weakest ” and “concede”, that gives the two parameters for this family) and opens new perspectives for belief merging. Some existing operators are also recovered as particular cases. Those operators can be seen as a special case of Booth’s Belief Negotiation Models [BOO 02], but the achieved restriction forms a consistent family of merging operators that worths to be studied on its own.

This paper provides a modal logic framework for reasoning about multi-agent belief and its fusion. We propose logics for reasoning about cautiously merged agent beliefs that have different degrees of reliability. These logics are obtained by combining the multi-agent epistemic logic and multisource reasoning systems. The fusion is cautious in the sense that if an agent’s belief is in conflict with those of higher priorities, then his belief is completely discarded from the merged result. We consider two strategies for the cautious merging of beliefs. In the first, called level cutting fusion, if inconsistency occurs at some level, then all beliefs at the lower levels are discarded simultaneously. In the second, called level skipping fusion, only the level at which the inconsistency occurs is skipped. We present the formal semantics and axiomatic systems for these two strategies and discuss some applications of the proposed logical systems. We also develop a tableau proof system for the logics and prove the complexity result for the satisfiability and validity problems of these logics.

Abstract not found