M-A. Williams. On the Logic of Theory Base Change. In Logics in Artificial Intelligence, C. MacNish, D. Pearce and L.M. Pereira (eds), LNCS No 835, 86 -- 105, Springer Verlag, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....belief bases. This alternative has been extensively studied and AGMlike operations have been defined for belief bases. However the term belief base has been used by two different communities with different meanings. Most authors interested in implementing AGM belief revision [ Nebel, 1990; Williams, 1994; Dixon, 1994 ] use belief bases to represent the belief set of an agent. A belief base in these approaches is a finite axiomatization of the theory (belief set) representing the agent s commitments. The fact that a formula of the belief set is an element of the belief base does not distiguish it ....

....7, and conclusions are presented in section 8. In the rest of the paper we will be working within a propositional framework, with a language L containing the basic boolean connectives. We will 2 Alternative approaches based on epistemic entrenchments (E bases [ Rott, 1991 ] ensconcements [Williams, 1994]) rely on a well behaved pre order of the beliefs in the base to construct operations of belief change. Given the pre order, the operations become less complex, but constructing and maintaining this pre order can be computationally very costly. vi RENATA WASSERMANN assume that a belief base is a ....

Mary-Anne Williams. On the logic of theory base change. In Proceedings of the European Workshop on Logics in Artificial Intelligence (JELIA'95), 1994.

.... of how to explicate them in terms of models of belief revision, see Gardenfors (1990) Doyle (1992) Rott (1996) del Val (1997) and Olsson (1997) Then we recall two ways of using entrenchment relations in theory change, the standard Gardenfors Makinson recipe and Rott s more brutal (Williams 1994) recipe. Neither of these can be sensibly used in conjunction with the positive relation . The negative relation is more suitable. If we use the GardenforsMakinson recipe for entrenchment based contraction with , then we satisfy the condition of Simple Filtering referring to basic ....

....has been quite popular in the literature. With minor variations, it has been suggested by Rescher (1964, pp. 49 50; 1976, pp. 18 19) Dubois and Prade (1991, Section 4; 1992, Section 3) Rott (1991b, Section 3; 1992a, Section 4, here without a connectedness presumption for #) and Williams (1994, Section 4) The positive generation mechanism should be viewed as a means of constructing an entrenchment relation from a finite representation of it, viz. from a prioritized belief base (or more exactly, from an E base satisfying a certain entailment condition, see Rott 1991b, pp. 142 146) ....

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Williams, Mary-Anne (1994): `On the Logic of Theory Base Change', in C. MacNish, D.

....thus a new epistemic entrenchment ordering needs to be the outcome of each revision. Later work extended this system to allow for iterated Belief Revision by allowing new information to be inserted with a ranking allocated upon insertion [13] and provided revision operations for theory bases [14]. These works allowed for an actual computer based implementation of iterated belief revision. However, like all Belief Revision, it still leaves much of the decision making (for example, whether to accept a new piece of information) to the user or calling application. Theory Extraction builds ....

....set of inconsistent beliefs, B , and a total preordering on B. Note that this is less restrictive than the requirements for an epistemic entrenchment ordering, which requires both that B be consistent, and that the ranking be such that there is no ff 2 B such that the set fx 2 B : x 6 ffg ff [14]. Theory Extraction produces a new set B 0 B such that B 0 6 where B 0 is in some sense minimally different from B. What is meant by minimality here is determined by the strategy being used, and generally involves ensuring that we lose fewer higher ranked beliefs where at all possible. ....

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Williams, M.A., On the Logic of Theory Base Change, in Logics in Artificial Intelligence, C. MacNish, D. Pearce and L.M. Pereira (eds), LNCS No 835, 86 -- 105, Springer Verlag, 1994.

....consequence relations can be represented by entrenchment relations. Entrenchment relations have a close relative in the study of belief revision, called epistemic entrenchment ( 18] Epistemic entrenchment proved to be a very useful for belief revision and became the standard tool ( 20] [52], 41] 42] for studying the AGM postulates ( 1] Moreover, generalizations of epistemic entrenchment have been proposed by Lindstrom Rabinowicz ( 34] and Rott ( 46] Lindstrom Rabinowicz proposed to drop linearity from epistemic entrenchment and used such a partial ordering for the study of ....

M.-A. Williams. On the logic of theory base change. In C. MacNish, D. Pearce, and L. M. Pereira, editors, Logics in Artificial Intelligence (JELIA '94), number 838 in Lecture Notes in Computer Science, pages 86--105, Berlin, 1994. Springer-Verlag.

....within the constraints imposed by the postulates. One major drawback with the AGM logic is that the operations all produce closed theories, which are usually infinite. Various solutions to this problem have been proposed, using finite theory bases to represent belief sets. See [Nebel, 1989; 1991; Williams, 1993] where the AGM postulates are weakened to provide more efficient revision algorithms. An implementation of Williams approach is described in [Dixon, 1993] 1.3 Motivation and Overview of the Paper One desirable property of any reasoning system is a means of expressing explicit justificational ....

Williams, M. (1993) On The Logic of Theory Base Change, CS Technical Report 459, University of Sydney.

....entrenchment ordering and a sentence , define cut ( f : g. The set cut ( contains all those sentences that are at least as entrenched as . An important property of an epistemic entrenchment is that it is a total preorder of the sentences in L such that the following theorem from [27] holds. Theorem 5. If is an epistemic entrenchment, then for any sentence , cut ( is a theory. Since a subtheory of a finitely axiomatizable theory may not be finitely axiomatizable we give the following result from [27] concerning a finite description of an epistemic entrenchment ....

....preorder of the sentences in L such that the following theorem from [27] holds. Theorem 5. If is an epistemic entrenchment, then for any sentence , cut ( is a theory. Since a subtheory of a finitely axiomatizable theory may not be finitely axiomatizable we give the following result from [27] concerning a finite description of an epistemic entrenchment ordering. In the next section we develop a computational model for change functions using a finite description of an epistemic entrenchment ordering, and the following theorem provides the theoretical basis for the one we adopt. ....

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M-A. Williams. On the Logic of Theory Base Change. In Logics in Artificial Intelligence, C. MacNish, D. Pearce and L.M. Pereira (eds), LNCS No 835, 86 -- 105, Springer Verlag, 1994.

....state, or epistemic state, is represented by an entrenchment ranking, formally defined below. It was shown in [Williams, 1994a] that entrenchment rankings can be used to support iterated belief revision for theories. Their partial specification can be used to support iterated base change revision [Williams, 1994b] and implementations based on this approach is described in [Williams it et al., 1995, Williams and Williams, 1997] Intuitively, an entrenchment ranking maps sentences to ordinals in O which is an ordinal chosen to be sufficiently large for the purpose of the discussion. Definition: An ....

Williams, M.A., On the Logic of Theory Base Change, in Logics in Artificial Intelligence, C. MacNish, D. Pearce and L.M. Pereira (eds), LNCS No 835, 86 -- 105, Springer Verlag, 1994.

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Williams, M.A., On the Logic of Theory Base Change, in the Proceedings of the Fifth European Workshop on Logics in Artificial Intelligence, LNCS No. 835, 86 -- 105, 1994.

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Mary-Anne Williams. On the logic of theory base change. In C. MacNish, D. Pearce, and L.M. Pereira, editors, Logics in Artificial Intelligence -- European Workshop JELIA'94, pages 86--105, York, UK, 1994. Springer-Verlag.

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