F. Donini, D. Nardi, and R. Rosati. Ground Nonmonotonic Modal Logics for Knowledge Representation. In Proceedings World Congress for AI (WOCFAI-95), 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....M 2 is the minimal model of P . This example rephrases the well known theory fLp pg of autoepistemic logic, and shows that intuitively weakly grounded stable models of GQLPs might exist. This can be handled by restricting attention to minimal stable models, in the spirit of ground logics [42, 11]. For programs like in the example, minimal stable models can be captured by means of a consequence operator, as shown in the next section. Notice that with respect to inference of positive literals, cautious reasoning from all stable models amounts to inference from the minimal ones; therefore, ....

F. Donini, D. Nardi, and R. Rosati. Ground Nonmonotonic Modal Logics for Knowledge Representation. In Proceedings World Congress for AI (WOCFAI-95), 1995.

.... result compare to other nonmonotonic logics, in particular, which nonmonotonic logic has similar complexity We know that Konolige s moderately grounded autoepistemic logic [ Konolige, 1988 ] and several other ground nonmonotonic modal logics have the same complexity [ Eiter and Gottlob, 1992; Donini et al. 1995 ] thus, we can use a theorem prover for such logics to perform abductive reasoning from default theories based on skeptical explanations. 4.2 Minimal explanations As mentioned above, one is usually interested in minimal explanations for observations. The results in [ Eiter and Gottlob, 1995 ....

F.M. Donini, D. Nardi, and R. Rosati. Ground Nonmonotonic Modal Logics for Knowledge Representation. In Proc. World Congress for AI (WOCFAI-95), 1995. Forthcoming.

....of a plain transformation. For the classes P 3 and P 3 , not many nonmonotonic logics of this complexity have been known until recently. It was known that moderately grounded AEL has this complexity [21] it appeared that a family of similar so called ground logics has the same complexity [19]. Moreover, the recent extension of default logic by trans epistemic defaults [50] is complete for P 3 resp. P 3 [51] Thus, the default abduction tasks in Table 1 that have this complexity can be eciently translated into this logics and vices versa; implementations lack today, however. ....

....hardness even for normal P. How does this result compare to other nonmonotonic logics, in particular, which nonmonotonic logic has similar complexity We know that Konolige s moderately grounded autoepistemic logic [36] and several other ground nonmonotonic modal logics have the same complexity [21, 19]; thus, we can use a theorem prover for such logics to perform abductive reasoning from default theories based on skeptical explanations. 4.2 Minimal explanations As mentioned above, one is usually interested in minimal explanations for observations. The results in [22] were that the complexity ....

F. Donini, D. Nardi, and R. Rosati. Ground Nonmonotonic Modal Logics for Knowledge Representation. In Proc. World Congress for AI (WOCFAI-95), 1995.

....of the semantic characterization above presented, with the aim of identifying the semantic counterpart to the fixpoint definition for every ground modal logic. Moreover, we are addressing the use of ground logics in knowledge representation: our first results in this direction are reported in [1, 2]. Acknowledgements We would like to thank Francesco Maria Donini for many discussions on the subject of the paper. ....

F. M. Donini, D. Nardi and R. Rosati. Ground Nonmonotonic Modal Logics for Knowledge Representation. To appear in Proceedings of WOCFAI-95.

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F. M. Donini, D. Nardi, and R. Rosati. Ground nonmonotonic modal logics for knowledge representation. In M. De Glas and Z. Pawlak, editors, Proceedings of the Second World Conference on the Fundamentals of Artificial Intelligence (WOCFAI-95), pages 133--144. Angkor, Paris, 1995.

....polynomial time algorithm using a polynomial number of calls to an NP oracle. Hence our method give an upper bound for non entailment in MDD logics that matches the corresponding lower bound and in this sense, we consider it optimal. For ground logics, entailment was proved Pi p 3 hard [5]. This third level of nondeterminism is due to the comparison of the objective knowledge of the player and the opponent models, which requires to solve another NP problem inside the second tableau we use the third tableau for this. In this case, our method could be turned into a Sigma p 3 ....

F. M. Donini, D. Nardi, and R. Rosati. Ground nonmonotonic modal logics for knowledge representation. In Proc. of WOCFAI-95, pages 133--144. Angkor, 1995.

....nonmonotonic character of the Work partially supported by Italian MURST 60 Tecniche di Ragionamento non Monotono . formalism is enforced by a preference criterion for selecting models based on the notion of minimal knowledge [8, 11] as in the case of the ground nonmonotonic modal logics [6, 9, 15, 20, 23]. Different forms of non first order reasoning can be captured in a modal epistemic language by identifying classes of epistemic sentences. In particular, for epistemic concept language, the modal operator has been first introduced in the query language to express queries to a first order concept ....

....the propositional language and LK is the propositional language augmented by the modal operator K. The resulting (nonmonotonic) consequence operator is defined as the intersection of all SG expansions for I. The above equation defines a family of nonmonotonic modal logics, called ground logics [6, 9, 20, 23]: for every normal modal logic S, the corresponding ground nonmonotonic modal logic SG is obtained by means of the above fixpoint equation. Ground nonmonotonic modal logics have also been given a semantic characterization in terms of a preference criterion among possible worlds described in ....

F. M. Donini, D. Nardi and R. Rosati. Ground Nonmonotonic Modal Logics for Knowledge Representation. To appear in Proceedings of WOCFAI-95.

....large subset of MDD logics. Conversely, the S5 logic of minimal knowledge states can be given a fixpoint characterization [27] which is a slight variation of McDermott and Doyle s equation, and which actually defines a whole family of logics of minimal knowledge states, the so called ground logics [23, 2]. Furthermore, the definition of a preference semantics for ground logics [20] has shown, from the semantical viewpoint, the existence of deep analogies between this family of formalisms and MDD logics. Finally, recent studies on the computational properties of the logic of minimal knowledge ....

....Furthermore, the definition of a preference semantics for ground logics [20] has shown, from the semantical viewpoint, the existence of deep analogies between this family of formalisms and MDD logics. Finally, recent studies on the computational properties of the logic of minimal knowledge states [2] have shown that reasoning in this logic is strictly harder (unless the polynomial hierarchy collapses to NP [9] than in all the most popular propositional nonmonotonic formalisms [1, 5] in particular wrt the most studied cases in MDD logics [14] Therefore the question arises of how similar ....

F. M. Donini, D. Nardi, and R. Rosati. Ground nonmonotonic modal logics for knowledge representation. In Proc. of WOCFAI-95, pp. 133--144. Angkor, Paris, 1995.

....polynomial time algorithm using a polynomial number of calls to an NP oracle. Hence our method gives an upper bound for non entailment in MDD logics that matches the corresponding lower bound, and in this sense we consider it optimal. For all ground logics, entailment is Pi p 3 hard [5]. This third level of nondeterminism is due to the comparison of the objective knowledge of the player and the opponent models, which requires to solve another NP problem inside the second tableau we use the third tableau for this. In this case, our method could be turned into a Sigma p 3 ....

....B is completed wrt (mcut) to prove that this can be done. We define MM(BP ) as the model obtained from any such S5 maximal model M by simply renaming each world with the valuation associated with it in M. The previous lemma and the properties of introspection consistent partitions of modal atoms [15, 5] lead to the following theorems. Theorem 19. Let L be a modal logic such that K L SW5 or K L KD45. If T is an LMDD expansion for Sigma , then there exists a modal consistent branch B of the tableau for CS5 (mcut) and global assumptions Sigma such that Th(MM(B) T . Theorem 20. ....

F. M. Donini, D. Nardi, and R. Rosati. Ground nonmonotonic modal logics for knowledge representation. In Proc. of WOCFAI-95, pages 133--144. Angkor, 1995.

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