S. Konieczny and R. Pino-Perez. Merging with integrity constraints. In Proc. of ESCQARU '99, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....beliefs based on semantically characterizing interpretations which are closest to some sets of interpretations. But the approach does not exploit any meta level information such as preferences. The approach has been generalized by considering merging with respect to integrity constraints [KP99] Another approach that extends belief revision theory, called arbitration operators, is by Liberatore and Schaerf [LS98] This form of merging is restricted to merging only two knowledgebases and it forces the result to be the disjunction of the two original knowledgebases. Also it does not use ....

....accepted or negated in the merged form. In contrast, these alternatives are concerned with using the priorities to preserve as much of the beliefs as is permitted without violating consistency. 5. 3 Knowledgebase merging techniques In addition to the techniques of Konieczny and Pino Perez [KP98, KP99] that we discussed in the previous subsection, we need to consider knowledgebase merging, by Baral et al. [BKMS92] which offers two approaches to combining prioritized theories. These two approaches assume a linear ordering over a set of sets of formulae. The first technique is top down merging ....

S Konieczny and R Pino Perez. Merging with integrity constraints. In Qualitative and Quantitative Approaches to Reasoning with Uncertainty, volume 1638 of Lecture Notes in Computer Science. Springer, 1999.

.... has been pointed out that the merging of information is similar to the operations studied in social choice theory where the aim is to provide fair and equitable methods for aggregating the preferences of the members of a society to produce a single relation reflecting the preferences of society [10, 14, 11, 15] it seems reasonable to expect that one rationality criterion for any proposed framework for the merging of information is that it be able to deal satisfactorily with the problems raised in social choice theory. The following example demonstrates the difficulty in devising a social ....

Sebastien Konieczny and Ramon Pino-Perez. Merging with Integrity Constraints. Unpublished manuscript, 1999.

....This section presents a new logical interpretation of Theory of Evidence. This interpretation is the one presented in [4] where we also proved some formal equivalences between the Maximum of Plausibility Strategy and one Knowledge Base Merging operator defined by Konieczny and Pino Perez [9] [8]. Let us first recall some definitions. 2.1 Preliminaries Definition 1. A multi set is a set where repeated occurrences of an element may exist. A knowledge set is a multi set of propositional formulas . Example 1. If A and B are propositional letters, then KS = B; AB; A; AB;AB] is a ....

S. Konieczny and R. Pino-Perez. Merging with integrity constraints. In Proc. of ESCQARU'99, 1999.

.... has been pointed out that the merging of information is similar to the operations studied in social choice theory, where the aim is to provide fair and equitable methods for aggregating the preferences of the members of a society to produce a single relation reflecting the preferences of society [10, 11]. It thus seems reasonable to expect any proposed framework for the merging of information to be able to deal satisfactorily with the problems raised in social choice theory. In this paper we investigate the link between the merging of epistemic states and two important impossibility results in ....

Sebastien Konieczny and Ramon Pino-Perez. Merging with Integrity Constraints. Unpublished manuscript, 1999.

....beliefs based on 17 semantically characterizing interpretations which are closest to some sets of interpretations. But the approach does not exploit any meta level information such as preferences. The approach has been generalized by considering merging with respect to integrity constraints [KP99] Another approach that extends belief revision theory, called arbitration operators, is by Liberatore and Schaerf [LS98] This form of merging is restricted to merging only two knowledgebases and it forces the result to be the disjunction of the two original knowledgebases. Also it does not use ....

....accepted or negated in the merged form. In contrast, these alternatives are concerned with using the priorities to preserve as much of the beliefs as is permitted without violating consistency. 5. 3 Knowledgebase merging techniques In addition to the techniques of Konieczny and Pino Perez [KP98, KP99] that we discussed in the previous subsection, we need to consider knowledgebase merging, by Baral et al. [BKMS92] which offers two approaches to combining prioritized theories. These two approaches assume a linear ordering over a set of sets of formulae. The first technique is top down merging ....

S Konieczny and R Pino Perez. Merging with integrity constraints. In Qualitative and Quantitative Approaches to Reasoning and Uncertainty, volume 1638 of Lecture Notes in Computer Science. Springer, 1999.

....a language and its semantics for representing information and axioms for characterizing the correct reasonings. And, in the context of beliefs modelling, many logical approaches have been proposed for reasoning with beliefs that one or several agents have about a situation [5] 6] 7] 8] 9] [10], 11] So, it is pertinent to point out the relations between, on the one hand, the numerical method for data fusion suggested by Dempster and, on the other hand, the logical methods suggested by logician people. We think that the first step is to reformulate the Theory of Evidence in logical ....

S. Konieczny and R. Pino-Perez. Merging with integrity constraints. In Proc. of ESCQARU'99, 1999.

....postulates. In Konieczny and Pino Perez [KP98] there is a proposal for merging beliefs based on semantically characterizing interpretations which are closest to the set of formulae to be updated. The approach has been generalized by considering merging with respect to integrity constraints [KP99] These proposals also maintain the primacy of updates. Another approach that extends belief revision theory, called arbitration operators, is by Liberatore and Schaerf [LS98] This form of merging is restricted to merging only two knowledgebases and it forces the result to be the disjunction of ....

....revisions. The key criticism with these approaches is the assumption that all the sources can be partially ordered without consideration of context. This does not seem realistic in practice. 6.1. 2 Knowledgebase merging techniques In addition to the techniques of Konieczny and Pino Perez [KP98, KP99] that we discussed in the previous subsection, we need to consider knowledgebase merging, by Baral et al. [BKMS92] which offers two approaches to combining prioritized theories. These two approaches assume a linear ordering over a set of sets of formulae. The first technique is top down merging ....

S Konieczny and R Pino Perez. Merging with integrity constraints. In Qualitative and Quantitative Approaches to Reasoning and Uncertainty, volume 1638 of Lecture Notes in Computer Science. Springer, 1999.

....regard that predicting the weather for that day is subject to a high degree of uncertainty and so prone to error. 20 6. 2 Acting on inconsistency There are various proposals for resolving inconsistency including truth maintenance systems [Doy79, Kle86] knowledgebase merging [BKMS92, CH97, KP98, KP99, LS98, CH99] and belief revision (starting with [AGM85, Gar88] and with developments including iterated belief revision [DP97, Leh95] and relationships with database updating [KM92] For a review of belief revision theory see [DP98] Yet we may not always want to immediately restore ....

S Konieczny and R Pino Perez. Merging with integrity constraints. In Anthony Hunter and Simon Parsons, editors, Qualitative and Quantitative Approaches to Reasoning and Uncertainty (ECSQARU'99), volume 1638 of Lecture Notes in Computer Science. Springer, 1999.

....a set of formulas) 4 IC (E) considered as the overall knowledge from the m sources given the integrity constraints IC. Recently, several families of such merging operators have been de ned and characterized in a logical way [ Revesz, 1997; Lin and Mendelzon, 1999; Liberatore and Schaerf, 1998; Konieczny and Pino P erez, 1999; Benferhat et al. 2000 ] Among them are the so called model based merging operators [ Revesz, 1997; Lin and Mendelzon, 1999; Liberatore and Schaerf, 1998; Konieczny and Pino P erez, 1999 ] where the models of 4 IC (E) are de ned as the models of IC which are preferred according to some ....

.... ned and characterized in a logical way [ Revesz, 1997; Lin and Mendelzon, 1999; Liberatore and Schaerf, 1998; Konieczny and Pino P erez, 1999; Benferhat et al. 2000 ] Among them are the so called model based merging operators [ Revesz, 1997; Lin and Mendelzon, 1999; Liberatore and Schaerf, 1998; Konieczny and Pino P erez, 1999 ] where the models of 4 IC (E) are de ned as the models of IC which are preferred according to some criterion depending on E. Often, such preference information take the form of a total pre order on interpretations, induced by a notion of distance d( E) between an interpretation and the ....

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S. Konieczny and R. Pino Perez. Merging with integrity constraints. In Proc. of ECSQARU'99, LNAI 1638, pages 233{ 244, 1999.

....de Ciencias Universidad de los Andes M erida Venezuela pino ciens.ula.ve Abstract We give in this paper new results on merging operators. Those operators aim to de ne the beliefs (or goals) of an agents group from the individuals beliefs (goals) Using the logical framework of [KP99] we study the relationships between two important sub families of merging operators: majority operators and arbitration operators. An open question was to know if those two families are disjoint or not. We show that there are operators that belong simultaneously to the two families. ....

.... framework for solve this belief (goals) aggregation step, is the use of knowledge merging operators [CH97, Cho98, BKMS92, LM99, Rev97, Kon00] In some related works di erent sets of logical properties that knowledge merging operators have to satisfy have been proposed [Rev97, LS98, LM99, KP98, KP99] Those logical characterisations are used to de ne a taxonomy of merging operators, that allows to compare di erent merging methods and to choose the method corresponding to the behaviour wanted in a particular application. We will focus on the merging with integrity constraints ....

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S. Konieczny and R. Pino Perez. Merging with integrity constraints. In Proceedings of the Fifth European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU'99), Lecture Notes in Arti - cial Intelligence 1638, pages 233-244, 1999.

....Le probl eme pos e par la fusion de E etant donn e IC est de caract eriser une formule 4 IC (E) consid er ee comme la croyance globale du groupe form e par les n sources fusionn ees. R ecemment, plusieurs familles d op erateurs de fusion ont et e d efinies et caract eris ees logiquement [24, 19, 17, 12, 13, 3]. Certains de ces op erateurs [24, 19, 17, 13] appel es parfois model based consistent a d efinir les mod eles de 4 IC (E) comme les mod eles pr ef er es de IC selon un crit ere d ependant de E. G en eralement, cette information pr ef erentielle est repr esent ee par un pr e ordre ....

....IC est de caract eriser une formule 4 IC (E) consid er ee comme la croyance globale du groupe form e par les n sources fusionn ees. R ecemment, plusieurs familles d op erateurs de fusion ont et e d efinies et caract eris ees logiquement [24, 19, 17, 12, 13, 3] Certains de ces op erateurs [24, 19, 17, 13] appel es parfois model based consistent a d efinir les mod eles de 4 IC (E) comme les mod eles pr ef er es de IC selon un crit ere d ependant de E. G en eralement, cette information pr ef erentielle est repr esent ee par un pr e ordre total sur les interpr etations, et elle est ....

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S. Konieczny and R. Pino P'erez. Merging with integrity constraints. In Proc. of ECSQARU'99, LNAI 1638, pages 233--244, 1999.

....protagonist to the best possible degree. In other words majority operators try to minimize global dissatisfaction whereas arbitration operators try to minimize individual dissatisfaction. The proofs have been omitted for space requirements but can be found in the extended version of this work [12]. We also provide a representation theorem a la Katsuno Mendelzon [9] and we show the close connections between belief revision and merging operators. In section 2 we state some notations. In section 3 we propose a logical definition of merging operators with integrity constraints, we de ne ....

....of commutative revision operators is very close to the one of belief revision operators. But it su ers two drawbacks from a merging point of view. First it allows to merge only two knowledge bases. And it forces the result to be in the disjunction of the two given knowledge bases. We argue in [11, 12] that it has not to be always the case. De nition 10. If 4 is an IC merging operator we de ne a commutative revision operator 4 by 4 = 4 ( t ) We will say that 4 is the commutative revision operator associated with 4. Theorem 9. If 4 is an IC merging operator, then the operator 4 ....

S. Konieczny and R. Pino Perez. Merging with integrity constraints. Technical Report 99-01, LIFL, 1999. http://www.li .fr/GNOM/articles/it9901.ps.

....bases and on the selection of some maximal subsets, due to a given order (not necessarily the inclusion) We study the logical properties of these operators. More exactly we investigate the rationality of these operators through the logical characterization of merging operators stated in [KP98, KP99] This characterization is useful to classify particular merging methods and to highlight aws and advantages of each of them. In particular, an important drawback of combination operators is that the source of each knowledge is lost in the fusion process. We shall call merging operators the ....

....; M 00 n;m i where M 00 j;k = M j [ M 0 k . So notice that if F = hM 1 ; Mn i and F 0 = F hP 1 ; Pm i with 8i P i inconsistent, then F F 0 . So, when considering a ock, we can focus only on its consistent knowledge bases. 3 IC MERGING OPERATORS In [KP98, KP99] a set of logical properties for merging operators is stated. We call operators satisfying these postulates Integrity Constraints merging operators (IC merging operators for short) Next we recall those postulates. De nition 8 Let E be a knowledge set, let IC be a knowledge base coding the ....

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S. Konieczny and R. Pino Perez. Merging with integrity constraints. In Proceedings of the Fifth European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU'99), LNAI 1638, pages 233-244, 1999.

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S. Konieczny and R. Pino-Perez. Merging with integrity constraints. In Proc. of ESCQARU '99, 1999.

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S. Konieczny and R. Pino-P'erez. Merging with Integrity Constraints In Proceedings of ESCQARU'99

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S. Konieczny and R. Pino-Perez. Merging with integrity constraints. In Proc. of ESCQARU'99, 1999.

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S. Konieczny and R. Pino-Prez. Merging with Integrity Constraints In Proceedings of ESCQARU'99

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S. Konieczny and R. Pino-Perez. Merging with integrity constraints. In Proc. of ESCQARU '99, 1999.

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Sebastien Konieczny and Ramon Pino-Perez. Merging with Integrity Constraints. In Proceedings of the Fifth European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU '99. Lecture Notes in Artificial Intelligence, volume 1638, pages 233--2448, 1999.

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