Merging with Integrity Constraints

Konieczny, Sébastien; Pérez, Ramón Pino

doi:10.1007/3-540-48747-6_22

Cited by 74 publications

(65 citation statements)

References 9 publications

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“…However, there is a correspondance one-to-one between the postulates presented here and those presented in [12,15]. This correspondance is stated as follows: for i = 0, 1, 2 the postulate ICi here corresponds to postulate ICi there.…”

Section: Remarkmentioning

confidence: 66%

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Merging operators: Beyond the finite case

Chacón

Pérez

2006

Information Fusion

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We extend the results of Konieczny and Pino Pérez (J. Log. and Comp. 2002) concerning merging operators in a finite logical framework to the infinite case (countably many propositional variables). The number of sources we consider remains finite. The main result is the representation theorem. In order to prove it, we state some results which are interesting for their own sake. Some postulates had to be restated in a new form. The new form is equivalent to the old one only in the finite case, but more appropriate to deal with the infinite case. The construction of merging operators starting from distances between valuations is also generalized. Indeed, we introduce a new kind of operators built upon the so called Cantor distance.

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Section: Remarkmentioning

confidence: 66%

“…Different sets of logical properties which have to be satisfied by belief merging operators, have been proposed [23,18,19,11,12]. These works offer a classification of (logical) merging operators.…”

Section: Introductionmentioning

confidence: 99%

Merging operators: Beyond the finite case

Chacón

Pérez

2006

Information Fusion

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“…Here, it means that two (or more) individuals can hold the same judgments on the propositions about which they have to express their view. merging on K. In this paper I will use the model-based merging operator introduced by Konieczny and Pino-Pérez (1999). 14 The idea of a model-based fusion operator is that models of F IC (K) are models of IC, which are preferred according to some criterion depending on K. Usually the preference information takes the form of a total pre-order (≤) on the interpretations induced by a notion of distance d(ω, K) between an interpretation ω and the profile K.…”

Section: The Formal Modelmentioning

confidence: 99%

Belief merging and the discursive dilemma: an argument-based account to paradoxes of judgment aggregation

Pigozzi

2006

Synthese

129

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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 escape-routes from the paradox -the so-called premise-based procedure and the conclusion-based procedure -are not, as I will show, satisfactory methods for group decision-making. 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 decision-making without paradoxes: a fusion approach".

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“…Postulate A6 states that if there is agreement between two merged profiles, then the merged aggregate profile should entail all the consequences the two merged profiles agree on. Note that this list has been enhanced in later publications, such as [7,8], to include integrity constraints, i.e. formulae that must be consistent with the result of the merging; for simplicity of exposition, we have used the simpler version that does not employ intergrity constraints.…”

Section: Background On Propositional Knowledge Mergingmentioning

confidence: 99%

“…In recent years, the area of knowledge merging has seen significant research results, both in proposals for specific merging operators [1,2,3,4,5] as well as in proposals for unifying frameworks, where specific merging operators can be seen as instantiations of these frameworks [6,7,8,9].…”

Section: Introductionmentioning

confidence: 99%

Merging First-Order Knowledge Using Dilation Operators

Gorogiannis

Hunter

Lecture Notes in Computer Science

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The area of knowledge merging is concerned with merging conflicting information while preserving as much as possible. Most proposals in the literature work with knowledge bases expressed in propositional logic. We propose a new framework for merging knowledge bases expressed in (subsets of) first-order logic. Dilation operators (a concept originally introduced by Bloch and Lang) are employed and developed, and by combining them with the concept of comparison orderings we obtain a framework that is driven by model-based intuitions but that can be implemented in a syntax-based manner. We demonstrate specific dilation operators and comparison orderings for use in applications. We also show how postulates from the literature on knowledge merging translate into our framework and provide the conditions that dilation operators and comparison orderings must satisfy in order for the respective merging operators to satisfy the new postulates.

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Merging with Integrity Constraints

Cited by 74 publications

References 9 publications

Merging operators: Beyond the finite case

Merging operators: Beyond the finite case

Belief merging and the discursive dilemma: an argument-based account to paradoxes of judgment aggregation

Merging First-Order Knowledge Using Dilation Operators

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