P. Revesz. On the semantics of theory change: Arbitration between old and new information. In C. Beeri, editor, Proceedings of the Twelth ACM Symposium on Principles of Database Systems, pages 71--82, Washington D.C., 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....In this section we briefly mention a few of these, some of which (namely [2, 11, 14] actually generalise further than us in that they consider the problem of simultaneously merging together n pieces of information where possibly n 2. A di#erence between the present approach and papers such as [11, 12, 15] is that the latter are interested only in fair merging, i.e. they assume that the merging should always give equal precedence to the pieces of information involved, regardless of their source. In the case of binary merging which we consider this forces the merge operator to be commutative. Other ....

P. Z. Revesz, On the semantics of theory change: Arbitration between old and new information, in Proceedings of the Twelfth ACM SIGACT SIGMOD SIGART Symposium on Principles of Database Systems (PODS'93) (1993) 71--82.

....that is obtained by running T in the A system together with an i optimizer [respectively, together with a c optimizer] s.t. Insert = Insert . 6 Related works Coherent integration and proper representation of amalgamated data is extensively studied in the literature (see, e.g. [8, 12, 22, 24, 25, 31 34, 38, 41]) Common approaches for dealing with this task are based on techniques of belief revision [31] methods of resolving contradictions by quantitative considerations (such as majority vote [32] or qualitative ones (e.g. de ning priorities on di erent sources of information or preferring certain ....

P.Z.Revesz. On the semantics of theory change: Arbitration between old and new information. Proc. PODS'93 , pp.71-82, 1993.

....a consistent view of the world. This demand is often complicated by the fact that such agents receive conflicting pieces of information from different sources. The process of combining possibly inconsistent pieces of information, known as merging, has started to receive more attention recently [7, 1, 2, 5, 6, 13, 12, 15]. In this paper we propose a framework for the modelling of merging operations. The proposal has its roots in the work of Spohn [14] Unlike most approaches we adopt a description of merging on the level of epistemic states instead of knowledge bases. In section 2 we give a brief introduction to ....

....merging operation assigns to the interpretations contained in that cell before normalisation. Figure 5 contains pictorial representations of these two majority operations. A is an appropriate generalisation of an example by Lin and Mendelzon [8] The latter was independently proposed by Revesz [13] as an example of weighted model fitting. The idea is simply to obtain the new plausibility ranking of an interpretation by summing the plausibility rankings given by the different epistemic states. AR is A refined by using consensus. Both A and An satisfy (E1) E4) Comm) and (Maj) and neither ....

P. Z. 1{evesz. On the Semantics of Theory Change: Arbitration between Old and New Information. In Proceedings PODS '93, 12th ACM SIGACT SIGMOD SIGAIIT Symposium on the Principles of Database Systems, pages 71-82, 1993.

....to de ne the distance between an interpretation and the knowledge set. So, it is this aggregation step of the individual preferences (distances) in a global one that makes behaviour di erences between the families. The three families stated next are well known, the family has been used in [Rev93, Rev97] the family in [Rev97, LM99, KP99] and the 4 family in [KP98, KP99] De nition 4 Let be a knowledge set, I be an interpretation and d be a distance between interpretations. The Max, GMax distances are de ned respectively by: d d;Max (I ; max 2 d(I ; d d; I ....

P. Z. Revesz. On the semantics of theory change: arbitration between old and new information. In Proceedings of the 12 th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Databases, pages 71-92, 1993.

....on the important issue of how in this representation different knowledge bases KB 1 ; KB l can be combined into a single KB. Main problems studied. The semantical issue of combining knowledge bases, as well as closely related issues, have been studied in the recent literature, see e.g. [2, 1, 18, 41, 23, 36, 39, 7, 33]. We do not intend to discuss the same issue here; rather, we are interested in tools and algorithms at the operational level, which are needed for the implementation of a suitable semantics. In this context, a principal operation is taking the logical intersection of knowledge bases KB 1 ; ....

P. Z. Revesz. On the Semantics of Theory Change: Arbitration between Old and New Information. In Proc. ACM Symposium on Principles of Database Systems (PODS-93), pp. 71--79, 1993.

....knowledge knows that b is true whereas none of the expert knows it. This was called implicit knowledge in [8] However, simply put these knowledge bases together is a wrong way since there could be contradictions between some experts. Some logical characterizations of merging have been proposed [18, 19, 13, 14, 16, 15, 11]. In this paper we extend these works by proposing a logical characterization when the result of the merging has to obey to a set of integrity constraints. We de ne two subclasses of merging operators, namely majority merging and arbitration operators. The former striving to satisfy a maximum of ....

P. Z. Revesz. On the semantics of theory change: arbitration between old and new information. In Proceedings of the 12 th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Databases, pages 71-92, 1993.

....that what is obtained would properly re ect the combination of the distributed data on one hand , and would still be coherent (in terms of consistency) on the other hand. Coherent integration and proper representation of amalgamated data is extensively studied in the literature (see, e.g. [1, 3, 7, 13, 14, 20 23, 26, 29]) Common approaches for dealing with this task are based on techniques of belief revision [20] methods of resolving contradictions by quantitative considerations (such as majority vote [21] or qualitative ones (e.g. de ning priorities on di erent sources of information or preferring certain ....

P.Z.Revesz. On the semantics of theory change: Arbitration between old and new information. Proc. PODS'93 , 71-82, 1993.

....called the arbitration and denoted as john4robert. It seems reasonable that the arbitration is more de nite than the disjunction and that the result of arbitrating between john and robert implies y. The idea of arbitration and a rst formal study of its properties was rst done by Revesz in [10], where he discusses the properties that an arbitration operator should satisfy. In this paper we propose a di erent characterization of arbitration. In the style of the work on belief revision and update, we propose a set of postulates for arbitration and argue for their plausibility. ....

....= fx; zg J = fx; yg fx; yg fxg fy; zg Hence, the minimal di erences between J and models of a are (k; a) f(x) y; z)g, while (k; a) 1. Therefore, the models of k S a are I 2 , I 3 , and the single model of k D a is I 2 . 3 C. Revesz s De nition of Arbitration More recently, Revesz in [10] introduced the idea of arbitration of logical theories. The arbitration of two theories a and b (denoted as a4b) is a new theory that retains as much as possible of the information contained in a and b. This operation is very di erent from classical revision, because revision is not ....

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P. Z. Revesz, \On the semantics of theory change: Arbitration between old and new information", in Proceedings of the Twelfth ACM SIGACT SIGMOD SIGART Symposium on Principles of Database Systems (PODS-93), 1993, pp. 71-82.

...., min1 and min2 . At present we do not know of any syntactic versions of these two semantic merging operations that are more ecient than Rmax and Rmin , the operations provided by theorem 4.1. is an appropriate generalisation of an example in [9] which was independently proposed in [13]. 10] provides a syntactic version of in terms of lists of w s known as infobases and shows that it is linear in the sum of the sizes of the infobases. It can be shown that converting a partition into an infobase is linear in the size of the partition. Unfortunately the conversion of an ....

P. Z. Revesz. On the Semantics of Theory Change: Arbitration between Old and New Information. In Proceedings PODS '93, 12th ACM SIGACT SIGMOD SIGART Symposium on the Principles of Database Systems, pages 71-82, 1993.

....present we do not know of any syntactic versions of these two semantic merging operations that are more efficient than Rmax and Rmin , the operations provided by theorem 4.1. is an appropriate generalisation of an example in [Lin and Mendelzon, 1999] which was independently proposed in [Revesz, 1993] . In [Meyer, 2000] a syntactic version of is provided in terms of lists of wffs known as infobases and shows that it is linear in the sum of the sizes of the infobases. It can be shown that converting a partition into an infobase is linear in the size of the partition. Unfortunately the ....

P. Z. Revesz. On the Semantics of Theory Change: Arbitration between Old and New Information. In Proceedings PODS '93, 12th ACM SIGACT SIGMOD SIGART Symposium on the Principles of Database Systems, pages 71--82, 1993.

....kind of answer set with implicit contradiction removal between knowledge bases. While ordered logic does not provide weak negation, it can be simulated in the language [40] Observe that specific approaches for combining classical propositional and first order knowledge bases have been defined in [25, 130, 26, 106], while [27] has addressed the problem of combining default logic knowledge bases which must satisfy given integrity constraints. ELPs inherit this method by the correspondence between ELPs and default logic theories. Briefly, in terms of ELPs, the approach tries to retain as much as possible from ....

....removal method for conflicts that arise between consistent default theories of equal priority. The authors also extend their method to prioritized combination of default theories. Axioms for arbitration operators in the context of classical propositional knowledge bases have been addressed in [130] and [106] In [130] arbitration is defined as a model fitting operator, and it is shown that the axiomatic description of arbitration operators is incompatible with revision operators as in AGM theory [7] and update operators according to the theory in [92] On the other hand, in [106] axioms ....

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P. Revesz. On the Semantics of Theory Change: Arbitration between Old and New Information. Proceedings of the Twelfth ACM SIGACT SIGMOD-SIGART Symposium on Principles of Database Systems (PODS'93), pages 71--79, 1993.

.... is indeed the most interesting one (if all pieces of information can be put together without obtaining an inconsistency, we can simply do it) There is no consensus, in the literature, about the name to give to the operation of combining knowledge bases with the same degree of reliability: Revesz [15] and Liberatore and Schaerf [10, 11] use the name arbitration, while Lin and Mendelzon [13] and Lin [12] prefer the term merging. Konieczny and Pino Perez [8] show that there is a semantical distinction between arbitration and merging. Namely, they show that there are scenarios in which ....

....2 does not extend our knowledge about the previous time point. The litmus test example [3] shows a scenario in which such backward inference should be done. Let us now consider merging, or arbitration. This is the operation of integrating two knowledge bases having the same degree of reliability [15, 13, 10, 12, 11, 8]. The assumption is that the two knowledge bases refer to the same time point. Let the two knowledge bases be represented by the formulas K 1 and K 2 . It is straightforward to express them in brels: KB = # source(1) K 1 , source(1) K 2 # The result of arbitration or merging is the ....

P. Z. Revesz. On the semantics of theory change: Arbitration between old and new information. In Proceedings of the Twelfth ACM SIGACT SIGMOD SIGART Symposium on Principles of Database Systems (PODS'93), pages 71--82, 1993.

....try to minimize individual dissatisfaction, whereas majority operators try to minimize global dissatisfaction. One of our main concerns in this work is to state these intuitions in a formal way. Some operators quite close to merging operators have already been formally studied. Revesz defined in [Rev93, Rev97] model fitting operators which can be considered as a generalization of revision for multiple knowledge bases. Revesz also defined arbitration operators from model fitting operators. We make a criticism about Revesz s postulates: they do not distinguish between majority and arbitration. ....

....The second operator we consider is the 4 Sigma operator. This is a majority merging operator as we will see below. Lin and Mendelzon give it as an example of what they called operators of theory merging by majority in [LMa] Independently Revesz gives it as an example of weighted model fitting in [Rev93]. The Sigma operator comes from a natural idea: the distance between an interpretation and a knowledge set is the sum of the distances between this interpretation and the knowledge bases of the knowledge set. Definition 20 Let E be a knowledge set and let I be an interpretation we put: dist ....

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P. Z. Revesz. On the semantics of theory change: arbitration between old and new information. In Proceedings of the 12 th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Databases, pages 71--92, 1993.

....knowledge from each agent. In this paper, we propose a formal semantics for a generalization of the above problem merging first order theories. The approach has a close connection with the work on database updates [FUV83, FKUV86, KM91a] knowledge base revision [G 88, KM91b] and arbitration [Rev92, Rev97] It has a special property of retaining a maximal amount of information from each theory while observing the majority rule in case of conflict. We apply the semantics to merge the information in databases, where a database is viewed as a simple form of a first order theory in which facts, ....

....bases to contain inconsistencies, uncertainties and nonmonotonic modes of negation. Halpern and Moses [HM85] defined the notion of distributed knowledge held by a group of agents, but their formulation of distributed knowledge applies only to agents who do not have conflicting views. Revesz [Rev92] defined a new class of theory change operators called arbitration in which new information is considered equally credible as the old knowledge base. Arbitration deals with two knowledge bases only, one being the new information and the other the old knowledge base. This framework has been ....

P. Revesz. On the semantics of theory change: arbitration between old and new information. In Proceedings of the Twelfth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pages 71--82, 1992.

....one. Merging operators take two (or more) knowledge bases but give not necessarily preference to one of them, and the resulting knowledge base is as close as possible to the old knowledge bases. Some operators quite close to merging operators have already been formally studied. Revesz de ned in [Rev93, Rev97] model tting operators which can be considered as a generalisation of revision for multiple knowledge bases. Revesz also de ned arbitration operators from model tting operators. But Revesz s postulates do not distinguish between majority and arbitration. Liberatore and Schaerf have ....

....integrity constraints. Lin and Mendelzon give a 4 operator (when the distance chosen is the Dalal distance [Dal88] as an example of what they called operators of theory merging by majority in [LM] And independently, Revesz gives the same operator as an example of weighted model tting in [Rev93] This operator is indeed a majority merging operator as stated in the theorem below. First of all notice the following fact the proof of which is straightforward by de nition. Remark 17 d (I ; 1 t 2 ) d (I ; 1 ) d (I ; 2 ) Theorem 18 4 satis es postulates (IC0 IC8) Maj) ....

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P. Z. Revesz. On the semantics of theory change: arbitration between old and new information. In Proceedings of the 12 th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Databases, pages 71-92, 1993.

....(they also consider adding other restrictions on arbitration, but these are not geared towards fairness) 18] place an additional fairness requirement that amounts to requiring that when two inconsistent theories are merged each one has to give up something. Other research in the area includes [4, 7, 23]. Since we agree with [13] that the AGM setting is unclear on issues of interpretation, we consider it meaningless to argue that one interpretation the temporal one or the multi agent one is right and another wrong, only that one should be clear on one s interpretation and should explore its ....

Peter Z. Revesz. On the semantics of theory change: Arbitration between old and new information. In Proceedings of the Twelfth ACM SIGACT SIGMOD SIGART Symposium on Principles of Database Systems (PODS '93), pages 71-82, 1993.

....consider any of the sources completely unreliable, the best we can do is to merge the two views in a new and consistent one, trying to preserve as much information as possible. We call this merging process arbitration. A formal study of the properties of arbitration was first done by Revesz in [10], where he discusses the properties that an arbitration operator should satisfy. In this paper we critically review Revesz s work and propose a different characterization of arbitration. In the style of the work on revision and update, we propose a set of postulates for arbitration and then prove ....

....to the expansion Cn(k) a, but the new knowledge base (Cn(k) a) must be consistent if a is consistent. The contraction of a theory Cn(k) with respect to a formula a 2 Cn(k) written Cn(k) Gamma a, is a subset of Cn(k) that does not contain a. A new operation, recently introduced by Revesz in [10] is arbitration. The arbitration of two theory A and B is a new theory that if possible contains the starting sets A and B. This operation is different from classical revision, because the revision is not commutative: the second argument (a in the revision Cn(k) a) is more important than the ....

[Article contains additional citation context not shown here]

P. Z. Revesz. On the semantics of theory change: Arbitration between old and new information. In Proceedings of the Twelfth ACM SIGACT SIGMOD SIGART Symposium on Principles of Database Systems (PODS-93), pages 71--82, 1993.

....follows: find the models of A the models that are closest to T , i.e. find the models of A that are minimal w.r.t. T . Katsuno and Mendelson [9] showed that the Fagin et al. framework [6] satisfy the AGM postulates. Subsequently, many authors (e.g. Katsuno and Mendelson themselves [9] Revesz [16], Grahne et al. 8] have extended the AGM axioms to reflect new philosophical and semantical insights. The primary aim of our paper, however, is not to specify new schemes for updating databases. Rather, our aim is simply to highlight an important connection that database updating problems, ....

P. Revesz. (1993) On the Semantics of Theory Change: Arbitration between Old and New Information, Proc. 1993 ACM Symp. on Principles of Database Systems, pps 71--82.

....revision operators presented here is a generalization of the result in Katsuno Mendelzon [15] for non abductive revisions. Moreover, the domain theory is playing the role of an integrity constraint as modeled in [15] A similar approach could be used to study other operators such as the one in [21] in terms of abduction by trying to define new abductive change operators based on regular operators. The operators so defined do not preserve consistency ( Phi and ff can be consistent but Phi ffi a ff can be inconsistent) There are two sources (not necessarily independent) for the ....

P.Z. Ravesz. On the semantics of theory change: arbitration between old and new information. In Proc. 12th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pages 71--82, Washington, DC, 1993.

....for computing such extensions, which run in polynomial time if possible. Questions of this type arise in several areas, such as cluster analysis [2, 20] computational geometry [1] philosophy of science [17, 18, 13, 15] updating and revising theories [6, 25] arbitration between theories [19], and machine learning [12, 11, 26] The best known metric between subsets of a metric space is the Hausdorff metric, defined as d h (S 1 ; S 2 ) maxfmax e2S 1 min f2S 2 Delta(e; f) max e2S 2 min f2S 1 Delta(e; f)g: This metric is trivially computable in polynomial time, and it has ....

....the truthlikeness of the other theory. Notice that measuring theory distance in this setting has suggestive applications for theory revision (change a theory into the closest possible one that meets the revision) and arbitration between theories. An example can be drawn from the court domain (cf. [19]) Suppose that in a trial two testimonies (which can be represented as theories) are very similar while a third is much different. Given that the witnesses are independent of each other, the belief of the jury in the reliability of the third testimony will naturally decrease with growing distance ....

P. Z. Revesz. On the Semantics of Theory Change: Arbitration between Old and New Information. In Proceedings of the Twelth ACM SIGACT SIGMOD-SIGART Symposium on Principles of Database Systems (PODS-93), pages 71--79, June 1993.

....on the important issue of how in this representation different knowledge bases KB 1 ; KB n can be combined into a single KB. Main problems studied. The semantical issue of combining knowledge bases, as well as closely related issues, have been studied in the recent literature, see e.g. [2, 1, 18, 41, 23, 36, 39, 7, 33]. We do not intend to discuss the same issue here; rather, we are interested in tools and algorithms for operations at the technical level, which are needed for the implementation of a suitable semantics. In this context, a principal operation is taking the logical intersection of knowledge bases ....

P. Z. Revesz. On the Semantics of Theory Change: Arbitration between Old and New Information. In Proc. ACM Symposium on Principles of Database Systems (PODS-93), pp. 71--79, 1993.

....done while the author was visiting the University of Toronto. This research was supported by a grant from the Canadian Institute for Robotics and Intelligent Systems and an Oliver E. Bird Faculty Fellowship from the University of Nebraska Lincoln. A preliminary version of this paper appeared in [Rev93]. For correspondence write to revesz cse.unl.edu. Arbitration may be used to test against the knowledge base several possible hypotheses. For example, a jury may test several hypothetical reconstructions of the crime based on a knowledge base containing the witnesses testimonies. Similarly, a ....

....operator Alchourr on, Gardenfors and Makinson [AGM85, Gar88] give a set of axioms or postulates that every adequate revision operator should be expected to satisfy. Similarly, Katsuno and Mendelzon [KM92] present axioms for updates. Arbitration may be used also as a knowledge base change operator [Rev93]. Suppose the old information is a knowledge base K and the new information is a sentence OE. Both revision and update resolve possible conflicts between the two by giving priority to the new information. However, if neither the old nor the new information is preferred, then arbitration over the ....

P. Z. Revesz. On the semantics of theory change: Arbitration between old and new information. Proceedings of the Twelfth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pages 71--82, 1993.

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P. Revesz. On the semantics of theory change: Arbitration between old and new information. In C. Beeri, editor, Proceedings of the Twelth ACM Symposium on Principles of Database Systems, pages 71--82, Washington D.C., 1993.

No context found.

P. Z. Revesz. On the semantics of theory change: Arbitration between old and new information. In Proc. of PODS'93, pages 71--82, 1993.

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