R. Fagin, G. Kuper, J.D. Ullman, and M.Y. Vardi. Updating logical databases. Advances in Computing Research, 3:1--18, 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....as close as possible to the old one. These properties are intuitive requirements one can expect from revision operators. These operators and their properties have been formally studied in philosophy, artificial intelligence and databases [1, 12, 16] and several operators have already been proposed [5, 9, 27, 28, 25]. In general, revision is a complex process [8, 20] and is not efficiently computable. The problem is that revision operators usually handle theories closed under logical consequences. Then, the computation of (all the consequences of) the new theory according to the old one and to the new ....

....beliefs about the world. We would like to define the change produced by a definition describes the result of this change: consistent. So more generally than a set of facts L we are considering unordered tuples of sets of facts hL 1 ; Ln i called flocks in the literature [9]. Such flocks can be also seen as multisets. We define the concatenation of flocks Delta in the obvious way: hL 1 ; Ln i Delta hL def = hL 1 ; Ln ; L and we define the change produced in a flock by a new piece of information by the following hL 1 ; Ln i ....

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R. Fagin, G. Kuper, J.D. Ullman, and M.Y. Vardi. Updating logical databases. Advances in Computing Research, 3:1--18, 1986.

....use even though the inconsistency may locate only in a single proposition. While in our approach in this paper, kb 0 is treated exactly the same as the two kbs above and the problem of losing all the information in kb 0 is avoided. Also related to our topic are belief revision systems ( G 88, FKUV86, KM91] and truthmaintenance systems (e.g. Doy79] The approaches of belief revision systems are different from ours. In theirs some knowledge in the knowledge base is given up to resolve inconsistency, while in ours nothing is given up and reasoning is performed in the presence of ....

R. Fagin, G. M. Kuper, J. D. Ullman, and M. Y. Vardi. Updating logical databases. Advances in Computing Research, 3:1--18, 1986.

....to p. The second alternative causes s to be true in addition to p. In addition, both alternatives cause q to be true. It is not possible to come up with a belief revision semantics that would allow us to identify, in all situations, which of the two alternatives in the above example is better [AGM85, Dal88, EG92, FKUV86, Gar88, Gra91, KM91, Mar91, MS86, Neb91, RdK87, Win90]. So, normally we are forced to make a choice and almost all the update mechanisms proposed in the literature make a choice or leave it to the user to make a choice, where s he may have no way of knowing apriori which is the correct choice [BKSW91, Dec90, GL90, KM90, RB92, SI91, Tom88, TA91, ....

R. Fagin, G. M. Kuper, J. D. Ullman, and M. Y. Vardi. Updating logical databases. Advances in Computing Research, 3:1--18, 1986.

....g to E 2 = fK 2 1 ; K 2 n g such that f(K) K. Let E be a knowledge set, E n will denote the knowledge set E t : t E z n . The result of the combination operators investigated in this paper is a set of knowledge bases. These sets have been called ocks by Fagin et al. FKUV86] Note that ocks and knowledge sets are both sets of knowledge bases (in fact knowledge sets are multi sets) But the di erence is that in the case of knowledge sets, the sets denote di erent sources of information, whereas in ocks the sets denote alternatives about the result of a ....

....of a maxiconsistent is a drastic one: a maxiconsistent is ever good or bad for a knowledge base. Therefore, we can expect a more subtle way to evaluate a maxiconsistent. Such a problem has already been addressed in the literature. For example in the case of database update, Fagin et al. FUV83, FKUV86] proposed a notion of fewer change: De nition 12 Let K 1 ; K 2 and K be knowledge bases. 1. K 1 has fewer insertions than K 2 with respect to K if K 1 n K K 2 n K. 2. K 1 has fewer deletions than K 2 with respect to K if K n K 1 K n K 2 . 3. K 1 has fewer change than K 2 with respect to K ....

R. Fagin, G. M. Kuper, J. D. Ullman, and M. Y. Vardi. Updating logical databases. Advances in Computing Research, 3:1-18, 1986.

....and testing for equivalence of conditionals is PSPACE complete, however. Eiter and Gottlob [ 1993 ] analyzed the complexity of nested conditionals assuming a variant of the full meet base revision scheme. A revised base is represented by a set of belief bases (also called a flock of bases [ Fagin et al. 1986 ] consisting of all remainders extended by the revision formula. In evaluating iterated revisions which is necessary for evaluating nested conditionals they apply the scheme to all bases in the set. Using this approach, they show that right nested conditionals that correspond to iterated ....

Ronald Fagin, Gabriel M. Kuper, Jeffrey D. Ullman, and Moshe Y. Vardi. Updating logical databases. Advances in Computing Research, 3:1--18, 1986.

....Let ffi be a foundational operator, and suppose B # : is a singleton for every and . Then ffi satisfies (R6) The practical utility of having B # : be a singleton was already noted in [Neb89] and it becomes clearer when we consider the non deterministic syntaxbased approach advocated in [FKUV86] see also [Doy91] In this approach, each element of Psi # : where Psi is a finite sets of formulas, is taken to generate an alternative revised database; Psi ffi is taken to be a set of databases, namely the set f Gamma [ f g j Gamma 2 Psi # : g, each element of which represents a ....

....that the TO condition (equivalently, unambiguous prioritized revision) completely characterizes deterministic foundational operators. 4 Non determinism on the other hand allows for more flexible preference orderings among beliefs, and handles iterated revision better (see the proposal of [FKUV86] and the discussion of [Doy91] It would be 4 To verify the equivalence of TO and unambiguous prioritized revision, note: any arbitrary unambiguous prioritized ordering can be imposed on the set of basic beliefs of a TO operator without affecting the result of revision; conversely, because ....

Ronald Fagin, Gabriel M. Kuper, Jeffrey D. Ullman, and Moshe Y. Vardi. Updating logical databases. Advances in Computing Research, 3, 1986.

....operator in the Alchourr on Gardenfors Makinson sense; the other one satisfies the basic postulates for revision. Introduction Revision is the process of according an old knowledge base with a new evidence. It has been formally studied [1, 8, 10] and several operators have already been proposed [4, 7]. The problem is that, in general, revision is a complex process [6] and is not efficiently computable. In this paper, we investigate three change operators based on forward chaining. The use of forward chaining provides us with an efficient way for computing the revision of a knowledge base. ....

.... F 0 is not R consistent hF 1 [ F 0 ; Fn [ F 0 i where fF 1 ; Fng is the set of subsets of F which are maximal and R [ F 0 consistent So more generally than a set of facts F we are considering n tuples of sets of facts hF 1 ; Fn i called flocks in the literature [7]. We put hF 1 ; Fn i Delta hF 0 1 ; F 0 m i def = hF 1 ; Fn ; F 0 1 ; F 0 m i and hF 1 ; Fn i Pi R F 0 def = F 1 Pi R F 0 ) Delta (F 2 Pi R F 0 ) Delta Delta Delta (Fn Pi R F 0 ) In order to investigate the relation between Pi R ....

R. Fagin, G. Kuper, J.D. Ullman, and M.Y. Vardi. Updating logical databases. Advances in Computing Research, 3:1--18, 1986.

....be specified using insertions of fixed sets of assertions. Deletions of fixed sets are employed when specifying PEP; EPEP cannot be specified in this fashion since the environment transformers in EPEP are non monotonic. Our definition of insertions is similar to the one used in databases (e.g. see [14, 13]) To enable efficient implementation, unlike [14, 13, 30] our deletion operation of non fixed sets is ad hoc. 1.2.3 Conservative Approximations to PFA Problems Throughout the paper it is assumed that every control flow path is executable. A dynamic environment env is reachable at a point pt ....

....Deletions of fixed sets are employed when specifying PEP; EPEP cannot be specified in this fashion since the environment transformers in EPEP are non monotonic. Our definition of insertions is similar to the one used in databases (e.g. see [14, 13] To enable efficient implementation, unlike [14, 13, 30], our deletion operation of non fixed sets is ad hoc. 1.2.3 Conservative Approximations to PFA Problems Throughout the paper it is assumed that every control flow path is executable. A dynamic environment env is reachable at a point pt if there exists a path in the control flow graph from the ....

R. Fagin, J. Ullman, G. Kuper, and M. Vardi. Updating logical databases. Advances in Computing Research, 3:1--18, 1986.

....level without any reference to how information is represented or manipulated by the system. However, this seems to be difficult for belief revision. A large number of authors seem to believe that a knowledge level analysis of belief revision is impossible [ Diettrich, 1986; Fagin et al. 1983; Fagin et al. 1986; Ginsberg, 1986 ] Considerations of how beliefs are represented on the symbol level seem inevitable for belief revision. Reconsidering Newell s original intentions when he introduced the notion of the knowledge level, we note that the main idea was describing the potential for generating ....

....spelled out in the previous section, there are good reasons to perform belief revision on belief bases considering the propositions in the base as the basic beliefs. As a matter of fact, such operations were adopted in an analysis of update semantics for logical databases [ Fagin et al. 1983; Fagin et al. 1986 ] and in modelling counterfactual reasoning [ Ginsberg, 1986 ] Basically, revision ( and contraction ( on a belief base B is defined in the following way: B x def = 8 : C2(B#x) C If 6 x B otherwise (17) B x def = B :x) x (18) with B # x being the same operation ....

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Ronald Fagin, Gabriel M. Kuper, Jeffrey D. Ullman, and Moshe Y. Vardi. Updating Logical Databases. Advances in Computing Research 3: 1--18, 1986.

....user constraints and sets of primitive constraints is a function, that is, for each user constraint there is only one set of primitive constraints defining it according to the clauses. Otherwise there could be problems like those encountered in the view update scenario in deductive databases [11]. Also, the modification of a constraint can be seen as a deletion followed by an addition. Consider a constraint c of the form X in r to be retracted from a store S. If V (c) 6= that is, some variables are involved in its range) c may have been activated several times during the computation ....

R. Fagin, G. Kuper, J. Ullman, M. Vardi. Updating Logical Databases. Advances in Computing Research, vol.3, 1986. 42

....as close as possible to the old one. These properties are intuitive requirements one can expect from revision operators. These operators and their properties have been formally studied in philosophy, artificial intelligence and databases [1, 12, 16] and several operators have already been proposed [5, 9, 27, 28, 25]. In general, revision is a complex process [8, 20] and is not efficiently computable. The problem is that revision operators usually handle theories closed under logical consequences. Then, the computation of (all the consequences of) the new theory according to the old one and to the new ....

....hL 1 [L 0 ; Ln [ L 0 i otherwise where fL 1 ; Ln g is the set of subsets of L which are maximal and P [ L 0 consistent. So more generally than a set of facts L we are considering unordered tuples of sets of facts hL 1 ; Ln i called flocks in the literature [9]. Such flocks can be also seen as multisets. We define the concatenation of flocks Delta in the obvious way: hL 1 ; Ln i Delta hL 0 1 ; L 0 m i def = hL 1 ; Ln ; L 0 1 ; L 0 m i and we define the change produced in a flock by a new piece of ....

[Article contains additional citation context not shown here]

R. Fagin, G. Kuper, J.D. Ullman, and M.Y. Vardi. Updating logical databases. Advances in Computing Research, 3:1--18, 1986.

....or deletion of rules and constraints is treated as a normal update. In this dissertation, we advance the method of [JJ91] by the treatment of temporal constraints and the optimization of the computation of implicit updates. Here we should also note that work on the knowledge base update problem [FKUV86] Dal88] LLo89] KM90] Wut93] is relevant to the integrity maintenance problem, since, in the former, a knowledge base has to be changed to reflect the updates and maintain the constraints at the same time. However, most approaches to knowledge base updates do not distinguish between the ....

R. Fagin, G. Kuper, J. Ullman, and M. Vardi. Updating Logical Databases. Advances in Computing Research, 3:1--18, 1986.

....alternative revised databases in which the agent could believe only, but the theory cannot tell which. This does not mean that we need to move outside the theory of action to reason about revision; rather, it simply introduces a degree of non determinism in revision, analogous to the proposal of [8]. In fact, the connection between deterministic revision and AGM is very tight in our framework: theorem 4 tells us that any AGM operator can be captured in a theory of action that uniquely determines the revised database, and it can be shown that any theory of action that yields such ....

Ronald Fagin, Gabriel M. Kuper, Jeffrey D. Ullman, and Moshe Y. Vardi. Updating logical databases. Advances in Computing Research, 3, 1986.

....that for solving contradictions, or equivalently, restoring consistency, one has to reject information. In other terms, one has to express a preference between information in such a way that the rejected information is the least preferred. Many works have exploited this idea, among them are [12] [11], 14] 19] 17] 15] c fl 1998 L. Cholvy ECAI 98. 13th European Conference on Artificial Intelligence Edited by Henri Prade Published in 1998 by John Wiley Sons, Ltd. 18] 20] However, there are different ways for expressing a preference between information. One can order the ....

R. Fagin, G. Kupper, J. Ullman, and M. Vardi. Updating logical databases. Advances in Computing Research, 3, 1986.

....as a method to choose from among the minimal translations. We generalize contact address: Department of Electrical Engineering and Computer Science, University of WisconsinMilwaukee, Milwaukee, Wisconsin 53211, USA; email: angelo miller.cs. uwm.edu the concept of minimal translation in [2, 3] to translations involving probabilities. Intuitively, we prefer explanations that are more specific in terms of certainty. This means that explanations in which we are less ignorant are more preferable to those in which we are less sure of our knowledge. The tighter the estimate the more ....

....b j : d j ,r j ] m ig (b j ) j d j r j j . The measure of ignorance for a set S of base predicates, denoted as mig(S) is the sum of all m ig (b i ) for each b i 2 S. When a unique probability range is assigned to each base predicate in the pf edb, the notion of minimality w.r.t. set inclusion [2, 11, 3] can be generalized to the level of probabilistic satisfiability. For example, fb 1 : 0:5; 1] b 2 : 1; 1]g j= p fb 1 : 0:5; 1]g generalizes fb 1 g fb 1 ; b 2 g. Moreover, it is also true that given two sets of updates E and E , E j= p E iff E j= E . This follows since each base predicate is ....

R. Fagin, G. M. Kuper, G. D. Ullman, and M. Y. Vardi. Updating Logical Databases. Advances in Computing Research, 3, 1986.

....= n=L, where n is the number of views dependent on a base predicate. If k is the number of base predicates in the pf idb then P (B i ) 1 for all i = 1, k. When a unique probability range is assigned to each base predicate in the pf edb, the notion of minimality w.r.t. set inclusion [3, 4] can be generalized to the level of probabilistic satisfiability. For example, fb 1 : 0:5; 1] b 2 : 1; 1]g j= p fb 1 : 0:5; 1]g generalizes fb 1 g fb 1 ; b 2 g. Hence, given update translations T and T , T T iff T j= p T. If T 1 ; Tm is a finite sequence of translations s.t. 8i (T ....

R. Fagin, G. M. Kuper, G. D. Ullman, and M. Y. Vardi. Updating Logical Databases. Advances in Computing Research, 3, 1986.

....an overall problem solution. Ultimately, a single consistent view is required from a set of multiple views. Information fusion is the process of deriving this single consistent view. Whilst theoretical approaches such as belief revision [AGM85,Gar88,DP97] databases and knowledgebase updating [FKUV86,KM89,Win90,Som94] and combining knowledgebases (for example [DLP92,Mot93,BKMS92,BKMS91] are relevant, information fusion addresses a wider range of issues raised by practical imperatives in applications such as requirements engineering. The problem of information fusion appears in many fields, ....

R Fagin, G Kuper, J Ullman, and M Vardi. Updating logical databases. Advances in Computing Research, 3:1--18, 1986.

....result from the combination while retaining a maximal amount of 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 ....

....Name. The answer is d, as desired. 8 Related Work The topic of merging databases is closely related to the early work on database update and belief revision. There is a huge literature in these two areas. Pioneering work includes Fagin et al. s theory of updating logical databases [FUV83, FKUV86] Gardenfors s theory of revision [G 88] Borgida s mechanism of exception handling [Bor85] Abiteboul and Grahne s update semantics [AG85] etc. There is also a great deal of work on multidatabases and 15 schema integration. Bright et al. BAP92] and Batini and Lenzerini [BL86] put forward a ....

R. Fagin, G. M. Kuper, J. D. Ullman, and M. Vardi. Updating logical databases. Advances in Computing Research, 3:1--18, 1986.

.... b, then combining their knowledge yields b, even though neither one of them individually knows b. 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] and knowledge base revision [G 88, KM91b] It has a special property of obtaining maximal amount of information from each theory while observing majority rule in case of conflict. We apply the semantics to merge the information among databases, where a database is viewed as a simple form ....

....Name. The answer is d, as desired. 8 Related Work The topic of merging databases is closely related to the early work on database update and belief revision. There is a huge literature in these two areas. Pioneer work includes Fagin et al. s theory of updating logical databases [FUV83, FKUV86] Gardenfors s theory of revision [G 88] Borgida s mechanism of exception handling [Bor85] Abiteboul and Grahne s update semantics [AG85] etc. There is also a great deal of work on multidatabases and schema integration. Bright et al. BAP92] and Batini and Lenzerini [BL86] put forward a survey ....

R. Fagin, G. M. Kuper, J. D. Ullman, and M. Vardi. Updating logical databases. Advances in Computing Research, 3:1--18, 1986.

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