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 the problem of measuring the similarity or distance between two finite sets of points in a metric space, and computing the measure. This problem has applications in, e.g., computational geometry, philosophy of science, updating or changing theories, and machine learning. We review some of the distance functions proposed in the literature, among them the minimum distance link measure, the surjection measure, and the fair surjection measure, and supply polynomial time algorithms for the computation of these measures. Furthermore, we introduce the minimum link measure, a new distance function which is more appealing than the other distance functions mentioned. We also present a polynomial time algorithm for computing this new measure. We further address the issue of defining a metric on point sets. We present the metric infimum method that constructs a metric from any distance functions on point sets. In particular, the metric infimum of the minimum link measure is a quite int...

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).

The ability of Database Systems to cope with changing situations and information coming from different sources is crucial for their applicability in real-world scenarios. Recent work in the field of belief revision and update has provided us techniques to handle change. In this paper we introduce a different form of revision aiming at capturing the process of "merging" possibly inconsistent pieces of information. We call this process arbitration. Along the lines of Gardenfors' work, we propose a set of postulates for this operator and prove a representation theorem. Keywords: knowledge representation, belief revision, non-monotonic reasoning. 1 Introduction One of the main challenges of today's software and databases systems is their ability to manage a large amount of information coming from different sources and at different moments in time. Advanced databases systems must cope with a changing world and not completely reliable sources of information by adopting a "principled" strat...

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.

We introduce an abductive method for a coherent integration of independent datasources.