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Merging Information Under Constraints: A Logical Framework
, 2002
"... We consider the problem of merging several belief bases in the presence of integrity constraints. ..."
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Cited by 76 (10 self)
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We consider the problem of merging several belief bases in the presence of integrity constraints.
Belief merging and the discursive dilemma: An argumentbased account to paradoxes of judgment aggregation
 Synthese
, 2006
"... 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 ..."
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Cited by 36 (8 self)
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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 escaperoutes from the paradox — the socalled premisebased procedure and the conclusionbased procedure — are not, as I will show, satisfactory methods for group decisionmaking. 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 decisionmaking without paradoxes:
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
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.
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.
On Merging StrategyProofness
 In Proceedings of the Ninth Conference on Principles of Knowledge Representation and Reasoning
, 2004
"... 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 lyi ..."
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Cited by 13 (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 a fair merging process even when some of them are not sincere. In fact, when strategyproofness 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 strategyproof landscape for many merging operators from the literature, including modelbased ones and formulabased 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.
Logic Based Merging
 J PHILOS LOGIC( 2011) 40: 239–270
, 2011
"... Belief merging aims at combining several pieces of information coming from different sources. In this paper we review the works on belief merging of propositional bases. We discuss the relationship between merging, revision, update and confluence, and some links between belief merging and social ch ..."
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Cited by 10 (2 self)
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Belief merging aims at combining several pieces of information coming from different sources. In this paper we review the works on belief merging of propositional bases. We discuss the relationship between merging, revision, update and confluence, and some links between belief merging and social choice theory. Finally we mention the main generalizations of these works in other logical frameworks.
Ten philosophical problems in deontic logic
 Normative Multiagent Systems, volume 07122 of Dagstuhl Seminar Proceedings. Internationales Begegnungsund Forschungszentrum für Informatik (IBFI), Schloss Dagstuhl
, 2007
"... Abstract. The paper discusses ten philosophical problems in deontic logic: how to formally represent norms, when a set of norms may be termed ‘coherent’, how to deal with normative conflicts, how contrarytoduty obligations can be appropriately modeled, how dyadic deontic operators may be redefined ..."
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Cited by 9 (4 self)
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Abstract. The paper discusses ten philosophical problems in deontic logic: how to formally represent norms, when a set of norms may be termed ‘coherent’, how to deal with normative conflicts, how contrarytoduty obligations can be appropriately modeled, how dyadic deontic operators may be redefined to relate to sets of norms instead of preference relations between possible worlds, how various concepts of permission can be accommodated, how meaning postulates and countsas conditionals can be taken into account, and how sets of norms may be revised and merged. The problems are discussed from the viewpoint of input/output logic as developed by van der Torre & Makinson. We argue that norms, not ideality, should take the central position in deontic semantics, and that a semantics that represents norms, as input/output logic does, provides helpful tools for analyzing, clarifying and solving the problems of deontic logic.
A Splitcombination Method for Merging Inconsistent Possibilistic Knowledge Bases
, 2004
"... In this paper, a new method for merging multiple inconsistent knowledge bases in the framework of possibilistic logic is presented. We divide the fusion process into two steps: one is called the splitting step and the other is called the combination step. Given several inconsistent possibilistic ..."
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Cited by 8 (5 self)
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In this paper, a new method for merging multiple inconsistent knowledge bases in the framework of possibilistic logic is presented. We divide the fusion process into two steps: one is called the splitting step and the other is called the combination step. Given several inconsistent possibilistic knowledge bases (i.e. the union of these possibilistic bases is inconsistent) , we split each of them into two subbases according to the upper free degree of their union, such that one subbase contains formulas whose necessity degrees are less than the upper free degree and the other contains formulas whose necessity degrees are greater than the upper free degree.