D. Zhang, Belief revision by sets of sentences, Journal of Computer Science and Technology, 1996, 11(2), 108-125.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....entailment. Firstly, while there have been several papers published concerned with iterated revision by single sentences, and also some concerned with revision by sets of sentences, there seems to be little in the way of any systematic study of iterated revision by sets Either directly (e.g. Zha 96] or indirectly, via the study of contraction by a set of sentences (e.g. FH 94] See [Gar 88] for a description of contractions and their close relationship with revision. of sentences. Darwiche and Pearl [DP 97] provide a postulational approach to the question of iterated revision of ....

D. Zhang, Belief revision by sets of sentences, Journal of Computer Science and Technology 11(2) (1996) 1--19.

....5 3 General Belief Revision Zhang et al. 1997) presented an extended system of AGM s theory which enables a treatment of belief revision by sets of sentences, especially infinite sets. The extended revision and contraction operators were called general ones. A set of postulates was introduced in [15][16] to model the general revision operation. A function Omega for belief set K and set of sentences F in L is called a general revision function if it satisfies the following nine postulates: Omega 1) K Omega F = Cn(K Omega F ) Omega 2) F K Omega F: Omega 3) K Omega F ....

Dongmo Zhang, Belief revision by sets of sentences, Journal of Computer Science and Technology, 11(2), 1996, 108-125.

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D. Zhang, Belief revision by sets of sentences, Journal of Computer Science and Technology, 1996, 11(2), 108-125.

....of information is represented as D = n, C , D = n, C, B , D = B , and D = B , then E = Cn( n, C, B ) is the unique extension of A = D, D , q) This could be argued to be reasonable. 2 Perfect Ordered Partition In order to describe degrees of reliability of information, Zhang in [7] introduced a notion of total ordered partition, which has been used to establish the general belief revision theory. In this paper we will reinforce this structure to specify the intended framework of default reasoning. Definition 2.1. Let F be a set of sentences, a partition of F, a ....

....for analyzing this process. Zhang eta . Is] presented an extended system of AGM s theory which enables a treatment of belief revision by sets of sentences, especially infinite sets. The extended revision and contraction operators were called general ones. A set of postulates was introduced in [7, 8] to model the general revision operation. A function O for belief set K and set of sentences F in L is called a general revision function if it satisfies the following nine postulates: O1) K O F: Cn(K O F) o2) c o . O3) KOFC K F. O4) If K 0 F is consistent, then K F C K O F. ....

Zhang Dongmo. Belief revision by sets of sentences. Journal of Computer Science and Technology, 1996, 11(2): 108-125.

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D. Zhang, Belief revision by sets of sentences, Journal of Computer Science and Technology, 1996, 11(2), 108-125.

.... Nanjing, 210016, China e mail:aics nuaa.edu.cn Abstract This paper aims to develop further and systemize the theory of multiple belief change based on the previous work on the package contraction, developed by [Fuhrmann and Hansson 1994] and the general belief changes, developed by [Zhang 1996]. Two main representation the orems for general contractions are given, one is based on partial meet models and the other on nice ordered partition models. An additional principle, called Limit Postulate, for the general belief changes is introduced which specifies properties of infinite ....

....sets of new beliefs, especially with infinite sets. A number of studies on extending and generalizing these operations so as to enable a treatment of belief change by sets of sentences then come out [Fuhrmann 1988] Niederde 1991] Rott 1992] Hansson 1992] Fuhrmann and Hansson 94] Zhang 1995] [Zhang 1996]. The ex tended operators for expansion, contraction and revision are usually called multiple ones while the original operators are referred to as singleton ones. A framework for multiple belief changes is not only interesting but also useful. We will benefit from it at least in the following ....

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Zhang Dongmo, Belief revision by sets of sen- tences, Journal of Computer Science and Technology,

....includes the classical first order logic with the standard interpretation. The notation means the classical first order derivability and Cn the corresponding closure operator, i.e. A 6 Cn(F) if and only if F A 2 Total ordered Partitions In order to capture the idea of strength of belief, [5] introduced the concept of total ordered partitions, which was a key notion in the establishment of general belief revisions (see [6] and the analyses of relationships between belief revision and nonmonotonic reasoning(see [7] In this section, we use the concept to specify reconstruction and ....

....partitions, which was a key notion in the establishment of general belief revisions (see [6] and the analyses of relationships between belief revision and nonmonotonic reasoning(see [7] In this section, we use the concept to specify reconstruction and cognitive process. Definition 2. 1 [5] Let F be a set of sentences, 7 ) be a partition of F, and be a total ordering relation on 7 ) The triple Z = F,7) is called a lolal orderedparlilion(TOP) ofF, or a lolalordered partition model. If is a well ordering on 7 ) E is called a well ordered partition (WOP) ofr. Intuitively, ....

Zhang Dongmo, Belief revision by sets of sentences, Journal of Computer Science and Technology, 1996, 11(2), 108-125.

.... I Introduction In recent years much work has been done on the relationship between nonmonotonic reasoning and belief revision [Makinson and G irdenfors 1991] Brewka 1991] Nebel 1992] Cravo and Martins 1993] Li 1993] G irdenfors and Makinson 1994] Boutflier 1994] G irdenfors and Rott 1995] [Zhang 1996]. A very close correspondence be tween them has been found based on the following formal translation: A I KC iff CK A The main idea is to identify revision of a belief set K by a proposition A with nonmonotonic inference from A under the guidance of the background knowledge K. With this ....

....the first question has been widely inves tigated in the literature [Makinson 1989] Freund 1990] Makinson 1993] Herre 1994] only the presentation of the extended rules is mostly in the Tarski style s inference operation C. As far as the generalization of belief revision are con cerned, [Zhang 1996] presented a kind of multiple revi sion framework, called general revision, which enables a treatment of revisions of belief set by arbitrary set of sentences. Zhang et al. 1997] further developed the framework by providing two presentation theorems and suggesting an additional postulate to ....

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Zhang Dongmo, Belief revision by sets of sentences, Journal of Computer Science and Technol- ogy, 1996, 11(2), 1-19.

....we will present a general framework for default reasoning , which can be viewed as a common generalization of the three approaches above. We prove that the syntax independent default reasoning in this framework is strictly identical to general belief revision operation, introduced by Zhang et al. [7] [8] This result provides a solution to the problem whether there is a correspondence between belief revision and default logic for the in nite case. As a by product, we also give an answer of the question, raised by Makinson and G ardenfors ( 6] of whether there is a counterpart contraction in ....

....Cg, D 0 2 = fA; C; Bg, D 0 3 = f:Bg, and D 0 4 = fBg, then E 0 = Cn(fA; C; Bg) is the unique extension of 0 = fD 0 1 ; D 0 4 g; This could be argued to be reasonable. 2 Perfect Ordered Partition In order to describe degrees of reliability of information, Zhang in [7] introduced a notion of total ordered partition, which has been used to establish the general belief revision theory. In this paper we will reinforce this structure to specify the intended framework of default reasoning. De nition 2.1 Let be a set of sentences, P a partition of , a wellordering ....

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Dongmo Zhang, Belief revision by sets of sentences, Journal of Computer Science and Technology, 11(2), 1996, 108-125.

....[Zhang et al. 97a] M) K F 1 K (F 1 [ F 2 ) Suppose that the nine postulates for the general belief revision implies ( M ) Consider a propositional language L with at least two propositional letters, say p and q. Let K = Cn(fp; qg) and = K; P, be a nice ordered partition of K(see [Zhang 96] where P = fCn(fqg) Cn(fp; qg)nCn(fqg)g. According to De nition 4.5 in [Zhang et al. 97a] we can have a general contraction function over K such that K f:pg = Cn(fqg) K f:p; qg = Cn(fp :q; p qg) Therefore, by Levi identity, we have K f:pg = Cn(f:p; qg) K f:p; qg = Cn(f:p; ....

.... each conditional knowledge base CB uniquely determines an ordering on Cn(B) Such ordering is nothing but the epistemic entrenchment in the terminology of [G ardenfors 88] and [G ardenfors and Makinson 88] In fact, it could be also some other kinds of ordering, such as nice ordered partition in [Zhang 96] and adventurousness in [Lehmann and Magidor 92] We use epistemic entrenchment here only because it is one of the most popular ones. This observation also shows that the inference in CB can be reduced to the classical logic and comparison of ordering (in nite inference can be transferred into ....

D. Zhang, Belief revision by sets of sentences, Journal of Computer Science and Technology, 1996, 11(2), 108-125.

....2 L such that j A and j :A can be entailed by the set of inference rules. In fact, the consistency of RN frames has been implied by the Theorem 4. 1 in [Zhang et al. 1997b] The authors proved it by translating the nonmonotonic derivability into the general (multiple) belief revision operation ( Zhang 1996a] and [Zhang et al. 1997a] The idea is to make the following correspondence between nonmonotonic inference and belief revision: j A i A 2 K where K is the set of nonmonotonic tautologies, that is, K = fB : j Bg: It is easy to see that this is a generalization of the relationship between ....

....the form: Aj B (see [Lehmann and Magidor 1992] 4 Note that the less ordering a formula is, the higher degree of belief it has. 9 9B 2 K( B 8C 2 K( C B C (C A C) C A) Sketch of proof. According to the de nition of , determines a niceordered partition of K (see [Zhang 1996a] and then a general revision function which satis es i) if K [ is consistent, K = K ; otherwise, ii) A 2 K i A 2 K and 9B 2 K( B 8C 2 K( C B C (C A C) C A) Therefore the theorem 1 implies what is desired. 2 This observation shows that nonmonotonic inference ....

D. Zhang, Belief revision by sets of sentences, Journal of Computer Science and Technology, 1996, 11(2), 1-19.

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