This work proposes an axiomatic characterization of merging operators. It underlines the differences between arbitration operators and majority operators. A representation theorem is stated showing that each merging operator corresponds to a family of partial preorders on interpretations. Examples of operators are given. They show the consistency of the axiomatic characterization. A new merging operator 4GMax is provided. It is proved that it is actually an arbitration operator. 1 Introduction In a growing number of applications, we face conflicting information coming from several sources. The problem is to reach a coherent piece of information from these contradicting ones. A lot of different merging methods have already been given [BI84, LMa, BKM91, BKMS92, Sub94]. Instead of giving one particular merging method we propose, in this paper, a characterization of such methods following the rationality of the postulates they satisfy. We shall call merging operators those meth...

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

We consider, in this paper, the problem of knowledge base merging with integrity constraints. We propose a logical characterization of those operators and give a representation theorem in terms of preorders on interpretations. We show the close connection between belief revision and merging operators and we show that our proposal extends the pure merging case (i.e. without integrity constraints) we study in a previous work. Finally we show that Liberatore and Schaerf commutative revision operators can be seen as a special case of merging.

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 process of integrating knowledge coming from diffeerent sources has been widely investigated in the literature. Three distinct conceptual approaches to this problem have been most succesful: belief revision, merging and update. In this paper we present a framework that integrates these three approaches. In the proposed framework all three operations can be performed. We provide an example that can only be solved by applying more than one single style of knowledge integration and, therefore, cannot be addressed by anyone of the approaches alone. The framework has been implemented, and the examples shown in this paper (as well as other examples from the belief revision literature) have been successfully tested.

We present a framework for non-prioritised belief revision --- i.e., belief revision in which newly acquired information is not always fully accepted --- in which the result of revision is arrived at via a kind of negotiation between old information and new. We show how both ordinary partial meet revision and Ferme and Hansson's selective revision can be captured in this framework, and also how it supports the definition of contraction operators which do not necessarily satisfy the basic AGM contraction postulate of (Success).

This paper presents an axiomatic approach to negotiation protocol analysis. We consider a negotiation procedure as multiple stages of mutual belief revision. A set of postulates in AGM-style of belief revision are proposed to specify rational behavior of negotiation. An explicit construction of negotiation function is given in which negotiation process is viewed as the interaction of two iterated revision operations. As a result the proposed axiomatic system is proved to be consistent. Finally, we examine our approach with an instantiation of Rosenschein and Zlotkin’s Monotonic Concession Protocol of Negotiation.

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

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.