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On the Logic of Merging
, 1998
"... 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 o ..."
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Cited by 111 (11 self)
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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...
Merging with Integrity Constraints
, 1999
"... 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 oper ..."
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Cited by 45 (10 self)
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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.
Syntactic Representations of Semantic Merging Operations
, 2001
"... Some recent research suggests that it is useful to conduct information merging on the level of epistemic states as an alternative to the usual approach of knowledge base merging [Benferhat et al., 1999; 2000; Meyer, 2000] . One way in which to represent epistemic states syntactically is in term ..."
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Cited by 5 (0 self)
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Some recent research suggests that it is useful to conduct information merging on the level of epistemic states as an alternative to the usual approach of knowledge base merging [Benferhat et al., 1999; 2000; Meyer, 2000] . One way in which to represent epistemic states syntactically is in terms of ranked knowledge bases. We discuss compact representations of ranked knowledge bases and provide a uniform method for obtaining syntactic representations of a large class of semantic merging operations which is linear in n times the product of the sizes of the n ranked knowledge bases to be merged. We show that the structure of some semantic merging operations can be exploited to provide methods for obtaining syntactic representations which are linear in the sum of the sizes of the n ranked knowledge bases to be merged. For others, the general method represents the best we can do in terms of computational complexity. 1
Syntactic Representations of Semantic Merging Operations
"... this paper we discuss syntactic representations of epistemic states in terms of two types of structures: ranked knowledge bases and partitions. Ranked knowledge bases, or Rbases, are discussed in section 2 and partitions in section 3. Section 4 is the heart of the paper. First, it provides a unifor ..."
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this paper we discuss syntactic representations of epistemic states in terms of two types of structures: ranked knowledge bases and partitions. Ranked knowledge bases, or Rbases, are discussed in section 2 and partitions in section 3. Section 4 is the heart of the paper. First, it provides a uniform method for obtaining syntactic representations of a large class of semantic merging operations in terms of partitions which is linear in n times the product of the sizes of the n partitions used in the merging process. Next, some semantic merging constructions proposed in the literature are considered [2, 10]. It is shown that for some of these we can obtain syntactic representations directly in terms of Rbases which are all linear in the sum of the sizes of the n Rbases to be merged. For some, however, it is shown that we can do no better than the general method in terms of computational complexity. Section 5 looks at related work and concludes
Belief Base Rationalization for Propositional Merging
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2011
"... Existing belief merging operators take advantage of all the models from the bases, including those contradicting the integrity constraints. In this paper, we show that this is not suited to every merging scenario. We study the case when the bases are ”rationalized” with respect to the integrity cons ..."
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Existing belief merging operators take advantage of all the models from the bases, including those contradicting the integrity constraints. In this paper, we show that this is not suited to every merging scenario. We study the case when the bases are ”rationalized” with respect to the integrity constraints during the merging process. We define in formal terms several independence conditions for merging operators and show how they interact with the standard IC postulates for belief merging. Especially, we give an independencebased axiomatic characterization of a distancebased operator.