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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 113 (12 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 46 (11 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.
Measuring inconsistency in knowledge via quasiclassical models
 In Proceedings of the National Conference on Artificial Intelligence (AAAI’02
, 2002
"... The language for describing inconsistency is underdeveloped. If a knowledgebase (a set of formulae) is inconsistent, we need more illuminating ways to say how inconsistent it is, or to say whether one knowledgebase is “more inconsistent” than another. To address this, we provide a general characteri ..."
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Cited by 28 (16 self)
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The language for describing inconsistency is underdeveloped. If a knowledgebase (a set of formulae) is inconsistent, we need more illuminating ways to say how inconsistent it is, or to say whether one knowledgebase is “more inconsistent” than another. To address this, we provide a general characterization of inconsistency, based on quasiclassical logic (a form of paraconsistent logic with a more expressive semantics than Belnap’s fourvalued logic, and unlike other paraconsistent logics, allows the connectives to appear to behave as classical connectives). We analyse inconsistent knowledge by considering the conflicts arising in the minimal quasiclassical models for that knowledge. This is used for a measure of coherence for each knowledgebase, and for a preference ordering, called the compromise relation, over knowledgebases. In this paper, we formalize this framework, and consider applications in managing heterogeneous sources of knowledge.
Negotiation as mutual belief revision
 In Proceedings of AAAI’04
, 2004
"... 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 AGMstyle of belief revision are proposed to specify rational behavior of negotiation. An explicit construction of nego ..."
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Cited by 19 (8 self)
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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 AGMstyle 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 StrategyProofness Landscape of Merging
 In Proceedings of the Fifth European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU’99), LNAI 1638
, 1999
"... 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 ly ..."
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Cited by 18 (5 self)
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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, strategyproof operators are highly desirable in order to guarantee equity among agents even when some of them are not sincere. In this paper, we draw the strategyproof landscape for many merging operators from the literature, including modelbased ones and formulabased ones. Both the general case and several restrictions on the merging process are considered. 1.
Quota and Gmin merging operators
 In Proc. of IJCAI’05
, 2005
"... 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 multiset of bases). ..."
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Cited by 17 (3 self)
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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 multiset of bases). Different interpretations of the “sufficiently many” give rise to specific operators. Each Gmin operator is parameterized by a pseudodistance 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, strategyproofness, and discriminating power. Those two families are shown as interesting alternatives to the formulabased merging operators (which selects some formulas in the union of the bases). 1
Representing and Aggregating Conflicting Beliefs
 Journal of Artificial Intelligence Research
, 2003
"... We consider the twofold problem of representing collective beliefs and aggregating these beliefs. ..."
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Cited by 17 (0 self)
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We consider the twofold problem of representing collective beliefs and aggregating these beliefs.
Distancebased merging: A general framework and some complexity results
, 2001
"... 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 inve ..."
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Cited by 17 (6 self)
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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 distancebased 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 distancebased operators are considered and their complexity is identified. Finally, distancebased merging operators are investigated from the logical point of view.
Approaches to measuring inconsistent information
 Inconsistency Tolerance. Volume 3300 of Lecture Notes in Computer Science
, 2005
"... Abstract. Measures of quantity of information have been studied extensively for more than fifty years. The seminal work on information theory is by Shannon [67]. This work, based on probability theory, can be used in a logical setting when the worlds are the possible events. This work is also the ba ..."
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Cited by 15 (8 self)
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Abstract. Measures of quantity of information have been studied extensively for more than fifty years. The seminal work on information theory is by Shannon [67]. This work, based on probability theory, can be used in a logical setting when the worlds are the possible events. This work is also the basis of Lozinskii’s work [48] for defining the quantity of information of a formula (or knowledgebase) in propositional logic. But this definition is not suitable when the knowledgebase is inconsistent. In this case, it has no classical model, so we have no “event ” to count. This is a shortcoming since in practical applications (e.g. databases) it often happens that the knowledgebase is not consistent. And it is definitely not true that all inconsistent knowledgebases contain the same (null) amount of information, as given by the “classical information theory”. As explored for several years in the paraconsistent logic community, two inconsistent knowledgebases can lead to very different conclusions, showing that they do not convey the same information. There has been some
Belief base merging as a game
 Journal of Applied NonClassical Logics
, 2004
"... 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 ..."
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Cited by 15 (9 self)
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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.