T. Eiter and G. Gottlob. On the complexity of propositional knowledge base revision, updates, and counterfactuals. AIJ, 57(2-3):227--270, October 1992.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....case can be found in [31] Those papers concentrate on the computation of the models of the revised theory, i.e. the repairs in our case. Inference or query answering is not addressed. The complexity of belief revision and counterfactual inference was exhaustively classified by Eiter and Gottlob [41]. They deal with the propositional case only. We have outlined above how to reduce in some cases consistent query answering to the propositional case by grounding. However, grounding of integrity constraints results in an update formula which is unbounded, i.e. whose size depends on the size ....

.... in some cases consistent query answering to the propositional case by grounding. However, grounding of integrity constraints results in an update formula which is unbounded, i.e. whose size depends on the size of the database. This prevents the transfer of any of the PTIME upper bounds from [41] into our framework. Similarly, the lower bounds from [41] require kinds of formulas di#erent from those that we use. The classic paper on updating logical theories by Fagin et al. 42] focuses on the semantics of updates but does not address computational issues. Moreover, the proposed framework ....

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T. Eiter and G. Gottlob. On the Complexity of Propositional Knowledge Base Revision, Updates, and Counterfactuals. Artificial Intelligence, 57(2-3):227-- 270, 1992.

....with integrity constraints. Our notion of minimal change is equivalent to that of Satoh [29] There are, however, several important differences between our work and past work on belief revision. Typically, belief revision considers revising a propositional theory with a propositional formula [20,12]. In our case we revise a single first order structure (a database instance) with a first order formula, often of a very restricted kind (e.g. functional dependencies) The program H r may be viewed as a representation of the revised database. However, the revised database is not explicitly ....

T. Eiter and G. Gottlob. On the Complexity of Propositional Knowledge Base Revision, Updates, and Counterfactuals. Artificial Intelligence, 57(2-3):227- 270, 1992.

....If IC is range restricted, then (DB, IC) is finite. 6 Queries to Inconsistent Databases In general, the number of all repair signatures can be exponential in the size (DB, IC) so using this theory directly is not likely to produce a good query engine. In fact, for the propositional case, [5] shows that the problem of deciding whether a formula holds in all models produced by Winslett s theory of updates [4] is # 2 complete. Since, as mentioned before, our repairs are essentially Winslett s updated models, the same result applies to our case. However, there are cases when ....

T. Eiter and G. Gottlob. On the Complexity of Propositional Knowledge Base Revision, Updates, and Counterfactuals. J. Artificial Intelligence, 57(2-3):227--270, 1992.

....P or R occurs negated in , it follows that, for any S P and any T R, M N [ S [ T is a model of . In particular, M [ N is a model of . This proves K . 3. Again, we only show 2 hardness of RSKEPTICAL and CSKEPTICAL . To this end, we exploit some results from [13] and [7; 8] Let P = fp 1 ; p n g and Q = fq 1 ; q m g be two distinct sets of variables, and consider a closed QBF of form 8P9Q , where is a propositional formula such that P [Q = Var( Furthermore, let R = fr 1 ; r n g be a set of variables distinct from Var( ....

....from Var( and let v be a further variable not occurring in Var( or R. For K and as defined in the proof of CCHOICE above, define the following knowledge base K S and formulas and : K S = K [ Q [ fvg; v ) q 1 : q m ) v) and = p i r i ) As shown in [13] , is valid iff v 2 K S s ( where s is the Satoh revision operator. Since s ( is equivalent to K S ( cf. 7; 8] we get that is valid iff v 2 K S ( 15) Hence, RSKEPTICAL is 2 hard. As for CSKEPTICAL , 2 hardness follows from ....

T. Eiter and G. Gottlob. On the Complexity of Propositional Knowledge Base Revision, Updates, and Counterfactuals. Artificial Intelligence, 57:227--270, 1992.

....case can be found in [30] Those papers concentrate on the computation of the models of the revised theory, i.e. the repairs in our case. Inference or query answering is not addressed. The complexity of belief revision and counterfactual inference was exhaustively classified by Eiter and Gottlob [40]. The paper [40] deals with the propositional case only. We have outlined above how to reduce in some cases consistent query answering to the propositional case by grounding. However, grounding of integrity constraints results in an update formula which is unbounded, i.e. whose size depends ....

....in [30] Those papers concentrate on the computation of the models of the revised theory, i.e. the repairs in our case. Inference or query answering is not addressed. The complexity of belief revision and counterfactual inference was exhaustively classified by Eiter and Gottlob [40] The paper [40] deals with the propositional case only. We have outlined above how to reduce in some cases consistent query answering to the propositional case by grounding. However, grounding of integrity constraints results in an update formula which is unbounded, i.e. whose size depends on the size of ....

[Article contains additional citation context not shown here]

T. Eiter and G. Gottlob. On the Complexity of Propositional Knowledge Base Revision, Updates, and Counterfactuals. Artificial Intelligence, 57(2-3):227-- 270, 1992.

....E and for every integer n, E denotes the multi set obtained by unioning E with itself n times. The complexity results we give in this paper refer to some complexity classes which we now brie y recall (see [ Papadimitriou, 1994 ] for more details) especially the classes 2 and 2 [ Eiter and Gottlob, 1992; Wagner, 1987 ] from the polynomial hierarchy PH, as well as the class BH 2 from the Boolean hierarchy (see [ Papadimitriou, 1994 ] Given a problem a, we denote by a its complement. We assume the reader familiar with the classes P, NP et coNP and we now introduce the following three classes ....

....(Hamming) Indeed, in this restricted case, 4 dH ;f;g IC (fKg) is equivalent to KD IC where D is Dalal s revision operator. The fact that the inference problem from K D IC is 2 hard (even in the restricted case where K is a conjunction of atoms) concludes the proof (see Theorem 6. 9 from [ Eiter and Gottlob, 1992 ] 2 hardness results. We show that these 2 hardness results hold in the restricted case where each K i is a singleton, reduced to a conjunction of literals (hence f is irrelevant) when g = lex by the following polynomial reduction M from max sat asg odd : to any propositional formula ....

T. Eiter and G. Gottlob. On the complexity of propositional knowledge base revision , updates, and counterfactuals. Arti cial Intelligence, 57(2-3):227-270, 1992.

....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 information is generally prohibitive. One solution is to ....

T. Eiter and G. Gottlob. On the complexity of propositional knowledge base revision, updates and counterfactuals. In Proc. of 11th Symposium on Principles of Database Systems, pp. 261--273, ACM Press, 1992.

.... on a minimal distance function as used by Winslett for knowledge base update [39] More precisely, Winslett in her pos sible models approach defines the knowledge base change operator o for the update of a propositional knowledge base K by a propositional formula p by Zod(op) U mEo( In [16], Eiter and Gottlob present complexity results for propositional knowl edge base revision and update. According to these results, Winslett s update operator is on the second level of the polynomial hierarchy in the general case (i.e. without any syntactic restriction on the propositional ....

....a logical consequence of the update by p of a knowledge base T is 2 complete. Update General case General case Horn Horn arbitrary p I I P l I k arbitrary p I I P l I k Top q H2 complete co NP complete co NP complete O(ll T II II q In the above table, we resume the results reported in [16]. The table contains five columns. In the general case (columns two and three) T is a general propositional knowledge base. In the Horn case (columns four and five) it is assumed that p and q and all formulas in T are conjunctions of Horn clauses. Columns two and four account for cases where no ....

Eiter, T. and Gottlob, G. On the Complexity of Propositional Knowledge Base Revision, Updates, and Counterfactuals. Artificial Intelligence, 57 (1992) 227-270.

....les multi ensembles. Soit un ensemble de croyances E, E k d enote le multi ensemble obtenu en faisant l union de E avec lui meme k fois. Les r esultats de complexit e que nous donnons dans cet article font mention de certaines classes de complexit e, en particulier Delta 2 et Theta 2 [7, 25] de la hi erarchie polynomiale PH, ainsi que la classe BH 2 de la hi erarchie bool eenne (voir [22] pour plus de d etails) Etant donn e un probl eme a, nous d enotons par a le probl eme compl ementaire de a. Nous supposons que le lecteur connait les classes P, NP et coNP et nous introduisons ....

....par r eduction depuis maxsat asg odd . Les r esultats de Theta 2 difficult e restent valables lorsque E est atomique et sont d eduits facilement des r esultats de complexit e de l inf erence a partir d une base r evis ee selon l op erateur de r evision de Dalal [6] cf. th eor eme 6. 9 de [7]) Enfin, dans le cas d = dD , le r esultat de Delta est d eriv e de celui de la r evision syntaxique linear base (th eor eme 5.9 de [21] et les r esultats de Theta sont d eriv es de la complexit e de la r evision syntaxique a maximisation de la cardinalit e (th eor eme 5.14 de [21] ....

T. Eiter and G. Gottlob. On the complexity of propositional knowledge base revision , updates, and counterfactuals. Artificial Intelligence, 57(23) :227, 270 1992.

....with integrity constraints. Our notion of minimal change is equivalent to that of Satoh [29] There are, however, several important differences between our work and past work on belief revision. Typically, belief revision considers revising a propositional theory with a propositional formula [20,12]. In our case we revise a single first order structure (a database instance) with a first order formula, often of a very restricted kind (e.g. functional dependencies) The program Pi may be viewed as a representation of the revised database. However, the revised database is not explicitly ....

T. Eiter and G. Gottlob. On the Complexity of Propositional Knowledge Base Revision, Updates, and Counterfactuals. Artificial Intelligence, 57(2-3):227-- 270, 1992.

....is range restricted, then T (DB;IC) is finite. 6 Queries to Inconsistent Databases In general, the number of all repair signatures can be exponential in the size of T (DB;IC) so using this theory directly is not likely to produce a good query engine. In fact, for the propositional case, [5] shows that the problem of deciding whether a formula holds in all models produced by Winslett s theory of updates [4] is Pi P 2 complete. Since, as mentioned before, our repairs are essentially Winslett s updated models, the same result applies to our case. However, there are cases when ....

T. Eiter and G. Gottlob. On the Complexity of Propositional Knowledge Base Revision, Updates, and Counterfactuals. J. Artificial Intelligence, 57(2-3):227--270, 1992.

....IC is range restricted, then T (DB;IC) is nite. 6 Queries to Inconsistent Databases In general, the number of all repair signatures can be exponential in the size of T (DB;IC) so using this theory directly is not likely to produce a good query engine. In fact, for the propositional case, [5] shows that the problem of deciding whether a formula holds in all models produced by Winslett s theory of updates [4] is P 2 complete. Since, as mentioned before, our repairs are essentially Winslett s updated models, the same result applies to our case. However, there are cases when ....

T. Eiter and G. Gottlob. On the Complexity of Propositional Knowledge Base Revision, Updates, and Counterfactuals. J. Arti cial Intelligence, 57(2-3):227-270, 1992.

....At the same time as the methodological work on principles of belief revision appeared, actual operators have been proposed in the literature. We now recall some of the revision operators, classifying them into formula based and model based ones. A more thorough exposition can be found in [12]. We use the following conventions: the symmetric di erence between two sets S 1 , S 2 is denoted by diff(S 1 ; S 2 ) that is diff(S 1 ; S 2 ) S 1 S 2 ) S 2 S 1 ) while the expression jSj denotes the number of elements of the set S. If S is a set of sets, S denotes the set formed ....

....valid. This is a result that holds for all revision operators, we now focus on the four speci c ones de ned above. To obtain the complexity results we use the reductions to belief revision outlined above and the complexity results for belief revision operators presented by Eiter and Gottlob in [12]. In fact, the arbitration operator has exactly the same complexity of the corresponding belief revision one. Proposition 17: Let a, b and c be propositional formulae, then the problem of deciding whether a4b j= c holds, is P NP [O(log n) complete for 4 = 4D , 2 complete for 4 = f4S ; ....

T. Eiter and G. Gottlob, \On the complexity of propositional knowledge base revision, updates and conterfactuals", Arti cial Intelligence Journal, vol. 57, pp. 227-270, 1992.

....line, Goldszmidt and Pearl [16, 49] have shown that implementation and characterization issues in belief revision can be realized through default knowledge. We refer to [16, 49] for more details. On the complexity side, a number of different revision approaches have been characterized, see e.g. [71, 76, 72, 64, 73]. In particular, the following reasoning problem has been considered there: Given a knowledge base, consisting of a set T of classical formulas, and classical formulas and , is it the case that is true in T after revision by This is also known as the Ramsey Test for conditional statements of ....

T. Eiter and G. Gottlob. On the complexity of propositional knowledge base revision, updates, and counterfactuals. Artificial Intelligence, 57(2--3):227--270, 1992.

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T. Eiter and G. Gottlob. On the complexity of propositional knowledge base revision, updates, and counterfactuals. AIJ, 57(2-3):227--270, October 1992.

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T. Eiter and G. Gottlob. On the complexity of propositional knowledge base revision, updates, and counterfactuals. Artificial Intelligence, 57:227--270, 1992.

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T. Eiter and G. Gottlob. On the complexity of propositional knowledge base revision, updates, and counterfactuals. Artificial Intelligence, 57(2-3):227--270, 1992.

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Eiter, T., and Gottlob, G. 1992. On the complexity of propositional knowledge base revision, updates and conterfactuals. Artificial Intelligence 57:227--270.

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T. Eiter and G. Gottlob. On the complexity of propositional knowledge base revision, updates, and counterfactuals. Articial Intelligence, 57:227270, 1992.

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Thomas Eiter and Georg Gottlob. On the complexity of propositional knowledge base revision, updates and counterfactuals. Technical report, Technical University of Vienna, July 1991.

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Eiter, T. and Gottlob, G. (1992) On the complexity of propositional knowledge base revision, updates, and counterfactuals. Art. Intell., 57, 227--270.

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T. Eiter and G. Gottlob. On the complexity of propositional knowledge base revision, updates, and counterfactuals. Artificial Intelligence, 57(2-3):227--270, 1992.

No context found.

Thomas Eiter and Georg Gottlob. On the complexity of propositional knowledge base revision, updates, and counterfactuals. Artificial Intelligence, 57:227--270, 1992.

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T. Eiter and G. Gottlob. On the complexity of propositional knowledge base revision, updates and counterfactuals. Artificial Intelligence, 57:227--270, 1992.

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T. Eiter and G. Gottlob. On the Complexity of Propositional Knowledge Base Revision, Updates, and Counterfactuals. J. Arti cial Intelligence, 57(2-3):227-270, 1992.

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