T. Eiter and G. Gottlob. The complexity of nested counterfactuals and iterated knowledge base revisions. Journal of Computer and System Sciences, 53:497512, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Ginsberg s operators is given. In fact, it can be compiled in CIRC and vice versa. Additionally, such result also holds for the case of iterated revision, i.e. when a polynomial number of revision steps is considered, by making use of the fact that also in this case the model checking is in co NP [10]. Finally, we remark that all of the non compilability results in [5, 6, 3] and some of those in [13] relies on the standard hypothesis that the polynomial hierarchy does not collapse. Moreover, the results in [6] hold if and only if this hypothesis is true. Operator Complexity Compactability ....

.... non compactability results of [5] we attempt to nd a trade ooe between compactability and the complexity of model checking of the Q Q Q Q Qk j j j j j3 CIRC CIRC j j j j j3 Q Q Q Q Qk PL Winslett, Borgida, Forbus, Satoh oe Dalal oe Weber oe WIDTIO oe Ginsberg [5] [14, 6, 10] [14] 6, 13] this paper Fig. 1. Results of the paper: the relative succinctness of belief revision operators, where means that the result also holds for iterated revision. knowledge base in which the original one is compiled. In particular, we consider the following ....

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T. Eiter and G. Gottlob. The complexity of nested counterfactuals and iterated knowledge base revisions. Journal of Computer and System Sciences, 53:497512, 1996.

....in a belief base describing the current context if a minimal change to the belief base to accept leads necessarily to the acceptance of . Based on this idea, the complexity of evaluating conditionals using different revision and update schemes has been analyzed [ Eiter and Gottlob, 1992; Eiter and Gottlob, 1993; Grahne and Mendelzon, 1995 ] Grahne and Mendelzon [ 1995 ] approached the problem by assuming a model checking framework in that the belief base is represented as a set of models. Based on this assumption, they derive polynomial algorithms for evaluating conditionals under Winslett s update ....

....a set of models. Based on this assumption, they derive polynomial algorithms for evaluating conditionals under Winslett s update scheme provided that the formula is fixed. Evaluating arbitrary (also nested) conditionals 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 ....

Thomas Eiter and Georg Gottlob. The complexity of nested counterfactuals and iterated knowledge base revisions. In Proceedings of the 13th International Joint Conference on Artificial Intelligence (IJCAI-93), pages 526--533, Chambery, France, August 1993.

....change process. We can now define the obvious belief change operation on extended belief sets in terms of the Ramsey test: E Delta = def f j 2 Eg; 2) for an extended belief sets E. Thus, Delta maps an extended belief set and a formula to an extended belief for similar reasons, in [Bou93, EG93]. 14 We might have defined Bel (I;sa) as f 2 L ( Phi) j (I; sa) j= B g, which would have been even more in the spirit of our definition of Bel (I; sa ) This definition agrees with our definition except when (I;sa) j= B(false) In this case, our definition does not put all formulas of ....

T. Eiter and Gottlob G. The complexity of nested counterfactuals and iterated knowledge base revisions. In Proc. Thirteenth International Joint Conference on Artificial Intelligence (IJCAI '93), pages 526-- 531, 1993.

....as belief revision, non monotonic inheritance networks and the axiomatic approaches to NMR. Nevertheless, we want to give some pointers to the complexity results presented in the literature. In the area of belief revision and update important results can be found in the works by Eiter and Gottlob [45, 43], Nebel [105, 106] and Grahne and Mendelzon [68] The complexity of reasoning in non monotonic inheritance networks has been analyzed by Horty, Thomason and Touretzky [71] Selman and Levesque [143] Geffner and Verma [55] Cadoli et al. 28] and Stein [149] Lehmann and Magidor in [83] give some ....

T. Eiter and G. Gottlob. The complexity of nested counterfactuals and iterated knowledge base revision. Technical Report CD-TR 92/44, Technische Universitat Wien, Vienna Austria, Christian Doppler Labor fur Expertensysteme, October 1992.

....the expression complexity to be in PSPACE. The quantifierfree case of our language does not have subjunctive implication operators in it, otherwise it would be a proper superset of the language in [GM95] For other complexity theoretic issues in belief revision and updates we refer the reader to [EG92, EG93, GM95]. 5 Expressive Power Let YF, SF, and SO be the class of all transformations from databases to databases expressible, respectively, by fixpoint queries, existential second order queries, and second order queries, as defined in [CH82, Var82] It is well known that YF is properly included in SF and ....

T. Eiter & G. Gottlob. The Complexity of Nested Counterfactuals and Iterated Knowledge Base Revisions. In: Proceedings of International Joint Conference on Artificial Intelligence, 1993.

....equivalence induced by a certain relation, and thus it is probably better characterized with one of the counting classes , such as #P. Note also that in this paper we have considered only the problem of revision, and not the related problem of update [GO95, FH94] Finally, we relate our work with [EG93]. In that paper, the authors analyze the complexity of inference in the (simple) iteration of the revision introduced by Fagin, Ullman and Vardi (also known as Ginsberg s revision) Other issues, related to the conditional logics are studied there. In our work, instead, we want to characterize the ....

T. Eiter and G. Gottlob. The complexity of nested counterfactuals and iterated knowledge base revisions. In Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence (IJCAI-93), pages 526--531, 1993.

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T. Eiter and Gottlob G. The complexity of nested counterfactuals and iterated knowledge base revisions. In Proc. Thirteenth International Joint Conference on Artificial Intelligence (IJCAI '93), pages 526--531, 1993.

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