G. Brewka. Preferred subtheories: An extended logical framework for default reasoning. In Proc. 11th International Joint Conference on Artificial Intelligence (IJCAI-1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....(see for example [MR70, BDP93, EGH95] One of the problems with reasoning with maximally consistent subsets is that there may be many of them. This can be ameliorated by assuming meta level information such as priorities over formulae. Here we consider some proposals based on this idea. In [Bre89] a knowledgebase Delta is a tuple ( Delta 1 ; Delta n ) where each Delta i is a set of classical formulae. Information in Delta i is preferred to (or more certain than) information in Delta j if i j. Given a knowledgebase Delta, a preferred subtheory Phi Delta is obtained using ....

....non empty subsets of Delta. Phi is preferred by stratification to Psi, denoted Psi strat Phi iff for all OE 2 Phi, and for all 2 Psi, In general, the democratically preferred subsets of a knowledgebase Delta are preferred subtheories of Delta (using the definition of [Bre89] and the preferred subtheories of Delta are stratification based preferred subsets of Delta. However, if is a total pre ordering, then demo coincide. We can compare this approach with ours, if we can generate an ordering over individual formulae based on the ranking of agents. Then ....

G Brewka. Preferred subtheories: An extended logical framework for default reasoning. In Proceedings of the Eleventh International Conference on Artificial Intelligence, pages 1043--1048, 1989.

....given about whether there is a counterpart contraction in nonmonotonic logic. Keywords nonmonotonic logic, default reasoning, belief revision 1 Introduction Reiter s default logic [x] is one of the most well developed systems of nonmonotonic reasoning. A number of variants of default logic [2 4] have been developed in the past several years. Poole s approach [4] is simple and natural. In his system facts and defaults are all represented by the classical first order language instead of adding some specific non classical rules. There is a disadvantage of Poole s approach, however, that it ....

....facts and defaults are all represented by the classical first order language instead of adding some specific non classical rules. There is a disadvantage of Poole s approach, however, that it does not allow to rep resent priorities between defaults. Brewka s preferred sub theories developed in [2, 5] have efficiently overcome this shortage. Nebel [3] combined both approaches of Poole and Brewka, and developed a system for default reasoning, called ranked default theory (RDT) As a very important result, Nebel established a relation between RDT and revised belief revision (called prioritized ....

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Gerhard Brewka. Preferred subtheories: An extended logical framework for default reasoning. In Proceedings of the 11th International Joint Conference on Artificial Intelligence, IJCAI-89, Sridharan N S (ed.), Morgan Kaufmann, 1989, pp.1034-1048.

....use of the selection of maximal consistent subsets of a belief base. This principle comes down to [Rescher and Manor, 1970] and is known under different names such as the possible world approach [Ginsberg and Smith, 1988] assumption based theories [Poole, 1988] supernormal default theories [Brewka, 1989] , syntax based approaches [Nebel, 1991] etc. We retain the last name and call the logic SBL . The language of SBL is defined as the set of all pairs ##, where # = 1 , # n ; #, # 1 , # n are propositional formulas from the language of CL. # represent the set of hard facts ....

G. Brewka. Preferred subtheories: an extended logical framework for default reasoning. In IJCAI'89, pages 1043-- 1048, 1989.

.... and Shoham, 1989] including for logic programming with negation as failure [Przymusinski, 1988] and terminological logics [Quantz and Royer, 1992] possibilistic logic [Dubois and Prade, 1988] syntax based belief revision formalisms, e.g. Nebel, 1989] and a variety of others, e.g. Brewka, 1989a] Brewka, 1989b] Brewka, 1994] Ginsberg, 1988] Zadrozny, 1987] Pollock, 1987] Konolige, 1988] Ryan, 1992b] Ryan, 1992a] Hunter, 1994] From a practical viewpoint, two very important kinds of non monotonic reasoning, in use even before the knowledge representation (KR) field of ....

G. Brewka. Preferred subtheories: An extended logical framework for default reasoning. In Proceedings of IJCAI-89, pages 1043--1049, Detroit, Michigan, 1989. 12

.... default knowledge (hereafter just default ) i.e. an expression of the form # # standing for if # then normally (or usually, or typically) # , as following from a given set of defaults. Several answers to this question have been proposed in the literature (such as in [BCDLP 93, BSS 95, Bre 89, GMP 93, Leh 95, LM 92, Pea 90, Wey 96] to # Supported by the DFG project Computationale Dialektik within the DFG research group Kommunikatives Verstehen . name but a few) but none of them (with the exception of [Wey 96] but see also Section 5 of this paper) seem to attempt any explicit ....

.... approach to default entailment As we said in Section 1 the lexicographic closure of # is but one member of a family of consequence relations , where , and, for all #, # In this section we briefly describe another member of this family which was given by Brewka in [Bre 89] Once again we base the ordering on the Z partition (# 0 , # n ) The idea is to use the following inclusion based ordering on We remark that this formulation of a sequence of revision steps in terms of a consequence relation is reminiscent of the vertical perspective of belief ....

G. Brewka, Preferred subtheories: An extended logical framework for default reasoning, in: N. S. Sridharan (ed.), Proceedings of the Eleventh International Joint Conference on Artificial Intelligence, (Morgan Kaufmann, 1989) 1043--1048.

....goal to an agent. That is, they are a symptom, not a cause. Any deductive account would thus be counterintuitive, and very likely false as well. 2 The abductive framework We have chosen to develop the proposed account of dialogue using the Prioritized Theorist framework [Poole et ai. 1987; Brewka, 1989; van Arragon, 1990] Theorist typifies what is known as a proof based approach to abduction because it relies on a theorem prover to collect the assumptions that would be needed to prove a given set of observations and to verify their consistency. This framework was selected because of ....

Gerhard Brewka. Preferred subthe- ories: An extended logical framework for default reasoning. In Proceedings of the 11th International Joint Conference on Artificial Intelligence, pages 1043-1048, Detroit, MI, 1989.

....it may happen, when using updating operators [1] that incorporating a new piece of information leads to a partially ordered knowledge. Another situation is when we merge multiple sources information. Indeed the application of some merging technique, like the one based on preferred sub theories [2], can also result in a set of partially ordered pieces of information. This paper proposes an extension of basic notions of possibilistic logic [3] when pieces of information are only partially ordered. Namely, instead of associating with formulas or interpretations numbers in [0, 1] we will ....

G. Brewka. Preferred subtheories: an extended logical framework for default reasoning. In Proc. of the 11th Inter. Joint Conf. on Artificial Intelligence (IJCAI '89), pages 1043--1048, 1989.

.... knowledge this is the first complete set of postulates for the revision of explicit nonmonotonic knowledge (of course we are aware of the close relationship between belief revision and nonmonotonic reasoning [8] as well as work showing that belief revision can be achieved using default reasoning [4]) Then we defined concrete revision and contraction operators, and showed that they fulfill the postulates, as well as adaptations of the Levi and Harper Identities. Our future work in the area will include the study of revision in defeasible logics with disjunction, and the examination of the ....

G. Brewka. Preferred Subtheories: An Extended Logical Framework for Default Reasoning. In Proc. 11th IJCAI, 1989, 1043-1048.

....problem of propositional logic can be mapped onto the energy minimization problem of a symmetric network and vice versa. But symmetric networks may be applied to propositional non monotonic reasoning as well [Pinkas, 1991a] To illustrate the approach consider the Meeting example taken from [Brewka, 1989] and assume the following commonsense statements. Usually one has to go to a project meeting. This rule does not apply if somebody is sick, unless he or she has a cold. The rule is also not applicable if somebody is on vacation. These statements can be formalized by five propositional ....

G. Brewka. Preferred subtheories: An extended logical framework for default reasoning. In Proceedings of the International Joint Conference on Artificial Intelligence, pages 1043--1048, 1989.

....naming defaults which simplifies both the notation and the implementation of the system (THEORIST) on which the formalism is based. He also introduces the notion of constraints, which we shall see in the following section, that can be used to rule out the applicability of some hypotheses. Brewka [10] generalises this framework by blurring the distinction between facts and defaults and allowing any number of partitions of formulae which, for practical purposes, can be considered linearly ordered when constructing extensions. Poole [103] also extends this approach by introducing a probabilistic ....

Gerhard Brewka. Preferred subtheories: An extended logical framework for default reasoning. In Proceedings of the Eleventh International Joint Conference on Artificial Intelligence, pages 1043--1048, 1989.

....has attracted extensive interest in the past decades. In fact, for almost every nonmonotonic approach there exist prioritised versions designed to handle preference information of some form (see, e.g. Gelfond et al. 1989; Konolige, 1988; Rintanen, 1994; Nebel, 1998; Eiter and Gottlob, 1995; Brewka, 1989; Brewka, 1996] Prioritised versions of default logic and logic programming 33 under the answer set semantics includes [Baader and Hollunder, 1993; Brewka, 1994; Rintanen, 1998b; Sakama and Inoue, 1996; Gelfond and Son, 1997; Zhang and Foo, 1997] as well as those approaches discussed earlier. ....

G. Brewka. Preferred subtheories: An extended logical framework for default reasoning. In Proceedings of the International Joint Conference on Artificial Intelligence, pages 1043--1048, 1989.

....supernormal default theory. E is the preferred extension of Delta if and only if E = C( Delta) It is obvious that there is always exactly one preferred extension. Note that the definition of this extension is fully constructive. It extends the notion of preferred subtheories as developed in [3] to the infinite case. 4.2 Prerequisite free default theories Can we simply extend the definition for supernormal defaults to this case The answer is obviously no. It may be the case that defaults are applied during the construction which are defeated later through the application of defaults ....

G. Brewka. Preferred Subtheor89ies: An Extended Logical Framework for Default Reasoning. Proc. IJCAI '89, pp. 1043--1048, 1989.

....6 RELATED WORK AND DISCUSSION We proposed a framework for belief revision where preference default theories together with a corresponding nonmonotonic inference relation are used to represent epistemic states and belief sets, respectively. Our underlying formalism draws upon ideas developed in [3] and [5] the notion of accepted conclusions introduced to guarantee consistency of belief sets and its application to belief revision is new. The framework is expressive enough to represent and reason about reliability and other properties of information. In [4] nonmonotonic belief bases in the ....

Brewka, G., Preferred Subtheories - An Extended Logical Framework for Default Reasoning, Proc. IJCAI-89, 1989

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G. Brewka. Preferred subtheories: An extended logical framework for default reasoning. In Proc. 11th International Joint Conference on Artificial Intelligence (IJCAI-1989.

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Brewka G.: Preferred subtheories: an extended logical framework for default reasoning. In Proc. of IJCAI'89, pp. 1043-1048, 2003.

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G.Brewka. Preferred Subtheories: An Extended Logical Framework for Default Reasoning Gesellschaft fur Mathematik und Datenverarbeitung. (in IJCAI, 1989).

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G. Brewka. Preferred subtheories: An extended logical framework for default reasoning. In IJCAI89, pages 1043--1048, Detroit, MI, 1989.

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G Brewka. Preferred subtheories: An extended logical framework for default reasoning. In Proceedings of the Eleventh International Conference on Artificial Intelligence, pages 1043--1048, 1989.

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G Brewka. Preferred subtheories: An extended logical framework for default reasoning. In Proceedings of the Eleventh International Conference on Artificial Intelligence (IJCAI'89), pages 1043--1048, 1989.

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G Brewka. Preferred subtheories: An extended logical framework for default reasoning. In Proceedings of the Eleventh International Conference on Artificial Intelligence (IJCAI'89), pages 1043--1048, 1989.

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G Brewka. Preferred subtheories: An extended logical framework for default reasoning. In Proceedings of the Eleventh International Conference on Artificial Intelligence (IJCAI'89), pages 1043--1048, 1989.

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G Brewka. Preferred subtheories: An extended logical framework for default reasoning. In Proceedings of the Eleventh International Conference on Artificial Intelligence (IJCAI'89), pages 1043--1048, 1989.

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G Brewka. Preferred subtheories: An extended logical framework for default reasoning. In Proceedings of the Eleventh International Conference on Artificial Intelligence, pages 1043--1048, 1989.

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G. Brewka, Preferred subtheories: an extended Logical framework for default reasoning, in: Proceedings IJCAI-89, (Detroit, Mich., 1989) 1034-1048

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Gerhard Brewka, Preferred subtheories: an extended logical framework for default reason- ing, in: Proceedings IJCAI-89, (Detroit, Mich., 1989) 1034-1048.

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