. Cayrol, Lagasquie-Schiex. Non-monotonic syntax-based entailment: a classification of consequence relations. Lecture notes in AI, 946, p. 107-114.1995. 14 F. Dupin de Saint-Cyr S. Loiseau  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... criterion generally makes use of uncertainty considerations by using explicitly uncertainty measures [Wilson93, Benferhat al95] or by using measures expressing priorities [Rescher64, Brewka89, Nebel91, Benferhat al93, Lehmann92] for a more detailed description of this kind of approach see [Cayrol Lagasquie95] These approaches consist in ranking the KB into priority levels (these levels are often supposed given by an expert (except in Pearl s system Z [Pearl90] where an automatic technique to rank the formulas is proposed, the algorithm is dedicated for KB in which formulas are default rules and the ....

. Cayrol, Lagasquie-Schiex. Non-monotonic syntax-based entailment: a classification of consequence relations. Lecture notes in AI, 946, p. 107-114.1995. 14 F. Dupin de Saint-Cyr S. Loiseau

....gives the following diagram ( meaning more general than ) FPL . NFPL EPL . SPL Interestingly, it lays in the second level of the polynomial hierarchy, like many problems in knowledge representation (including most nonmonotonic logics and belief revision see for instance [37] 49] [9]) Proposition 41 Deduction in NFPL is in Pi P 2 . Proof: let us call nfpl ded the problem of deciding whether ( fi) is a consequence of a NFPL formula Phi. The membership of the complementary problem nfpl cons to Sigma P 2 is given by the following nondeterministic algorithm: 1. guess ....

.... not idempotent, have been proposed for defining drowning free variants of possibilistic logic namely, leximin and discrimin [2] As for complexity, recall (Proposition 13) that nonmonotonic possibilistic entailment is in Delta P 2 (O(logn) then the leximin variant is in Delta P 2 (O(n) [9] and the discrimin variant is Pi P 2 complete [48] 9] This means that escaping the drowning effect generates an increase of complexity; as to practical computation, drowning free variants basically require computing some of the maximal consistent subsets of the knowledge base, which SPL does ....

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Claudette Cayrol and Marie-Christine Lagasquie-Schiex. Nonmonotonic syntax-based entailment: a classification of consequence relations, Proceedings of ECSQARU'95 (C. Froidevaux, J. Kohlas, eds.), Apringer Verlag, 107-114.

....imply #. This idea has been studied, among others, by Rescher, Fagin Ullman Vardi, Brewka, Nebel, Rott, del Val and several researchers from Toulouse. More methods of exploiting the structure for prioritized belief bases in processes of belief revision or nonmonotonic reasoning are surveyed in Cayrol and Lagasquie Schiex (1995). 8 How to use entrenchment relations in belief change In this section, we assume as given some relation of epistemic entrenchment over a theory K. The o#cial Gardenfors Makinson (1988) construction recipe for theory contraction based on epistemic entrenchment is this. Def . # # K . ....

Cayrol, Claudette, and Marie-Christine Lagasquie-Schiex (1995): `Non-monotonic Syntax-Based Entailment: A Classification of Consequence Relations', in C. Froidevaux and J. Kohlas (eds.), Symbolic and Quantitative Approaches to Reasoning and Uncertainty -- ECSQARU '95 , LNCS 946, Berlin: Springer, pp. 107--114.

....solving decision problems above NP. In the last part of the paper, we show that Binary Decision Diagrams [6] tools can be extended for solving some classes of coherence based entailment problems. 1 Other points of view such as cautiousness and validity of deduction rules have been considered in [8]. Chapter 2 Coherence based nonmonotonic entailment Throughout the paper, E denotes a non empty finite set of propositional formulae referred to as the belief base . E is not assumed to be consistent. Coherence based nonmonotonic entailment from a stratified belief base can be described as a ....

.... whose complexity is never beyond the second level of the polynomial hierarchy ( Delta p 2 , NP, co NP) Note that the computational complexity is not related to cautiousness: though Arg m is more cautious than Exi m and less cautious than Uni m, Arg m is more complex than Exi m and Uni m (see [8] for a study on this point of view) Considering the strength of the restrictions needed to reach polynomial complexity, we decided to try to tackle one specific entailment relation using an algorithmic tool which is dedicated to the resolution of propositional logic based NP hard problems: ....

Claudette Cayrol and Marie-Christine Lagasquie-Schiex. Non-monotonic syntax-based entailment: A classification of consequence relations. In C. Froidevaux and J. Kohlas, editors, Lecture Notes in Artificial Intelligence 946 (Proc. of ECSQARU-95), pages 107--114, Fribourg, Switzerland, 1995. Springer Verlag.

....in the general propositional case. Results are also provided in the three restricted cases of strictly ordered belief bases, of Horn bases (sets of conjunctions of Horn clauses) and of strictly ordered Horn bases. Even in 1 Cautiousness and validity of deduction rules have been considered in [8]. Cayrol, Lagasquie Schiex, Schiex NMR: Complexity Algorithms 3 restricted cases such as strictly ordered belief bases or Horn bases, the results are quite disappointing since the complexity in the worst case remains greater than the complexity of classical entailment unless both ....

....permits to distinguish the Uni Lex entailment, whose complexity never exceeds the Delta p 2 class. Note that the computational complexity is not related to cautiousness: though Arg m is more cautious than Exi m and less cautious than Uni m, Arg m is more complex than Exi m and Uni m (see [8] for a study on this point of view) Considering the strength of the restrictions needed to reach polynomial complexity, we decided to try to tackle one specific entailment relation using an algorithmic tool which is dedicated to the resolution of propositional logic based NP hard problems: ....

Claudette Cayrol and Marie-Christine Lagasquie-Schiex. Non-monotonic syntax-based entailment: A classification of consequence relations. In Lecture Notes in Artificial Intelligence 946 (Proc. of ECSQARU-95), pages 107--114, Fribourg, Switzerland, 1995.

....in (Gottlob 1992) First, we briefly present the entailment relations and the associated problems which will be considered from the computational complexity point of view. Secondly, we give 1 Other points of view such as cautiousness and validity of deduction rules havebeen consideredin (Cayrol Lagasquie Schiex 1995). an informal and simplified presentation of the main concepts of the complexity theory. Then, we provide comparative results. Even in restricted cases such as strictly ordered belief bases or Horn bases, the results seem to be disappointing since the complexity in the worst case remains greater ....

Cayrol, C., and Lagasquie-Schiex, M.-C. 1995. Non-monotonic syntax-based entailment: A classification of consequence relations.

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