Carlos Alchourron, Peter Gardenfors, and David Makinson. On the Logic of Theory Change: Partial Meet Contraction and Revision Functions. The Journal of Symbolic Logic, 50:510--530, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a change in epistemic state from the current state K to a new state K ff . Belief revision is the study of how this change is performed (see Figure 1.1) in particular, the nature of the new epistemic state. In the belief revision framework developed by Alchourr on, G ardenfors and Makinson [1, 31] (henceforth referred to as the AGM framework) three types of belief change are identified: belief expansion the epistemic input is added to the current epistemic state without removal of any existing beliefs We avoid the controversy surrounding whether the objects of beliefs are linguistic or ....

....ever being able to dismantle it in dry dock and reconstruct it from the best components. Pollock [101] notes that this metaphor is more in keeping with the negative coherence view. 2. 2 The AGM Framework for Belief Revision We shall base our study on the AGM framework for belief revision [1, 31, 32]. This approach is claimed, by G ardenfors [32] also [31] p. 35) to be coherentist in nature. The main reason for adopting this approach is that it is a well developed formal framework that should allow us to take advantage of a logical theory of abduction (to be discussed in Chapters 3 and 4) ....

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Carlos E. Alchourr on, Peter G ardenfors, and David Makinson. On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50:510--530, 1985.

....section the primary contribution of this paper addresses these issues. 3 An Alternative Approach to Expectations Our alternative approach to the definition of non monotonic inference relations via expectations orderings is embedded in a general theory of epistemic updating. The AGM theory [AGM85, GM88] of belief change takes into account the degree of currently held beliefs in assimilating new information, a rational agent should ensure that if some currently held beliefs must be given up, then, given the option, less firmly held beliefs may be given up in favour of more firmly held beliefs. ....

.... 6 : then K = Cn( 9 (9A ) If K [ f g 6 : but K : then K Cn(K [ f ; g) It is helpful to view K as the set of sentences that the evidence can explain given the background knowledge K. Properties (1 6R ) are basic postulates of the AGM revision operation [AGM85]. Postulate (6A ) says that if two pieces of evidence contain the same information relative to, and they do not conflict with, the current knowledge, then accepting them has the same effect on the current knowledge (this is a stronger postulate than (6R ) Postulates (7:1R 7:3A ) are several ....

Carlos E. Alchourron, Peter Gardenfors, and David Makinson. On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50:510--530, 1985.

....by comparing some current KRR systems and theories in terms of these new concepts and guidelines. Introduction Implemented knowledge representation and reasoning, KRR, systems run into danger when they attempt to implement traditional belief change theories intended for ideal reasoning agents [Alchourr on et al. 1985; Nebel, 1989; Hansson, 1993; 1999] Resource limitations can cause a system that guarantees consistency to fail. This is especially true with commonsense reasoning which requires a large knowledge base and a complex reasoning system. Due to this size and complexity, implemented commonsense ....

....and beliefs derived from those base beliefs. Belief change operations alter the base set of beliefs, and derived beliefs that lose their support are no longer believed. We are assuming that ALL the systems we will be discussing are using a foundations approach. By contrast, a coherence approach [Alchourr on et al. 1985] would allow previously derived beliefs to remain as long as they are not responsible for an inconsistency. even if their support was lost. Although our DOBS formalism follows the foundations approach, we offer a coherence version of the DOBS in Section 4.2 which would allow a coherence ....

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Carlos E. Alchourron, Peter Gardenfors, and David Makinson. On the logic of theory change: Partial meet contraction and revision functions. The Journal of Symbolic Logic, 50(2):510--530, June 1985.

....the revision of different theories (Theorem 4.3) We believe these results bring new light to the issue of how revision and update functions are related. They also provide a novel way to achieve iterated theory revision. 1 Overview Since they were introduced, the AGM notion of revision [1] and Katsuno and Mendelzon s update [5] have been considered two fundamentally different ways of changing knowledge. The usual interpretation is as follows ffl Revision takes place when new information is regarded as correcting our theory of a static world. According to revision, as little as ....

....62 K A then (K A) B K (A B) An intrinsic property of the AGM revision function is its non monotony. If one theory is included in another, the revision of the first is not necessarily included in the revision of the second: H K does not imply H A K A. Observation 2. 1 (follows from [1]) Given the basic postulates (K 1) K 6) for AGM revision, if is a revision operation in a language admitting at least two mutually independent formulae A; B (neither A 2 Cn(B) nor B 2 Cn(A) then monotony fails for . Proof. Let K = Cn(A; B) H 1 = Cn(A) H 2 = Cn(B) Assume monotony. As H i ....

Carlos Alchourr'on, Peter Gardenfors, and David Makinson. On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50:510--530, 1985.

....The field of Theory Change (or Belief Revision as it is also commonly known) is concerned with the study of ways of modifying a given state of affairs or theory, when new information about the situation is available. In 1985, the seminal paper of Alchourr on, Gardenfors and Makinson (AGM) [1] provided a specific way of modifying a logical theory given a single formula to be considered as the new information. This operation is known today as AGM revision and an extense literature on the topic followed their original work. Some years later, in 1991, Katsuno and Mendelzon [2] presented ....

....that satisfies the centering condition, such that [AB] S w2[A] fv 2 [B] v is w minimal in [B]g. Postulates (u6) and (u7) are superflous in presence of the rest. 3 Update for infinite languages Following the notion of a change operator advocated by Alchourr on, Gardenfors and Makinson [1], we generalize the update operation to theories. We redefine the update operator as a function that takes a theory and a formula and returns a theory, IK Theta L IK. Notice that in a finite propositional language this is just a notational variant of Katsuno and Mendelzon s original ....

Carlos Alchourr'on, Peter Gardenfors, and David Makinson. On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50:510--530, 1985.

....represented by means of nested intensional operators such as intentions to bring about belief. There exist important formal analyses of belief change outside the theories of rational interaction that we have reviewed up to now. Most prominent are AGM belief revision and KM update operations [1, 30]. Which of these different operations could apply to our example dialogue The official explanation [30, 23] says that when the hearer realizes that the speaker has changed his mind then he should update his beliefs, and when the hearer realizes that he had misunderstood an information from the ....

Carlos E. Alchourr'on, Peter Gardenfors, and David Makinson. On the logic of theory change: Partial meet contraction and revision functions. The Journal of Symbolic Logic, 50(2):510--530, June 1985.

.... [Gra91] On the contrary, if we suppose that nothing changes in the external word, and that an incoming piece of belief is supposed just to extend or correct our 8 current belief base then the picture is different, and it is claimed that one should use revision (understood as AGM revision of [AGM85]) Formally, update operations as defined in [KM92] are not only different from AGM revision operations, but even incompatible with them. That incompatibility leads to the question whether such a distinction is really acceptable. How can we decide whether an incoming information corresponds to a ....

Carlos Alchourr'on, Peter Gardenfors, and David Makinson. On the logic of theory change: Partial meet contraction and revision functions. J. of Symbolic Logic, 50:510--530, 1985.

....L. FERM E, Departamento de Computaci on, Universidad de Buenos Aires, Pabell on I Ciudad Universitaria (1428) Buenos Aires, Argentina. E mail: ferme dc.uba.ar Abstract In recent papers [10, 11] Krister Segerberg introduced Irrevocable Belief Revision, as closely related to AGM revision [2]. In this paper we present irrevocable belief revision in terms of an epistemic entrenchment relation. 1 Keywords: Logic of Theory Change, Irrevocable belief revision, Epistemic Entrenchment. 1 Background The AGM model [2] characterizes changes in the belief of a rational agent. AGM recognizes ....

....Irrevocable Belief Revision, as closely related to AGM revision [2] In this paper we present irrevocable belief revision in terms of an epistemic entrenchment relation. 1 Keywords: Logic of Theory Change, Irrevocable belief revision, Epistemic Entrenchment. 1 Background The AGM model [2] characterizes changes in the belief of a rational agent. AGM recognizes three di erent kind of change: expansion (that consists in adding a new belief) contraction (eliminating a belief from the belief corpus of the agent) and revision (adding new beliefs preserving consistency) Krister ....

Carlos Alchourron, Peter Gardenfors, and David Makinson. On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50:510-530, 1985.

....systems use such observations to update their representations, often by adjusting the (continuous) parameters in a Dirichlet distribution within a given belief net structure [Hec95] We, however, are making discrete changes to the structure of the Horn theory. Similarly, belief revision systems [AGM85, Dal88, Gar88, KM91] take as input an 2 (1) However, we make no claims concerning the applicability of our techniques to systems like KBANN [Tow91] which use a completely different means of modifying a theory. 2) The companion paper [Gre99] considers yet other ways of modifying a theory, viz. by rearranging the ....

Carlos E. Alchourr'on, Peter Gardenfors, and David Makinson. On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50:510--530, 1985.

.... as the commonsensical principle of selecting the best from the available set of alternatives [12] In a recent work [9] Nayak et al. have advocated the adoption of the principle of rejecting the worst in lieu of the principle of selecting the best in the context of AGM style belief revision [1, 3]. The aim of this work is to extend this idea to abductive reasoning in particular, to explore the consequences of discarding the choose the best principle in favour of reject the worst principle in the context of abductive belief change [10] This paper is organised as follows. In the next ....

....how abductive reasoning is a context with these features, and hence is appropriate for the reject the worst principle. 3 Abductive by Choosing the Best Recently a very interesting account of abduction has been offered by Pagnucco [10] as an extension of the classic AGM system of belief change [1]. We will briefly recount the AGM system of belief change followed by Pagnucco s account of abductive belief change. 3.1 Belief Change In the AGM system, a belief state is represented as a theory (i.e. a set of sentences closed under your favourite consequence operation) new information ....

Carlos E. Alchourron, Peter Gardenfors, and David Makinson. On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50:510--530, 1985.

....state axioms suffice for the simple domain we consider here. 4 These are axioms that only describe initial situations. Reiter [18] has 9; as the only initial situation, but to formalize belief, we need additional ones. 5 We shall restrict our attention to approaches in the AGM vein [1, 9, 11] although there are many others. AGM postulates [1, 9] for belief revision. By ( wemean the revision of belief state by new information . 6 (K 1) is deductively closed (K 2) A = K 3) B DC (K 4) If ) then EC B F= K ....

....here. 4 These are axioms that only describe initial situations. Reiter [18] has 9; as the only initial situation, but to formalize belief, we need additional ones. 5 We shall restrict our attention to approaches in the AGM vein [1, 9, 11] although there are many others. AGM postulates [1, 9] for belief revision. By ( wemean the revision of belief state by new information . 6 (K 1) is deductively closed (K 2) A = K 3) B DC (K 4) If ) then EC B F= K 5) G iff H (K 6) If H #JI , ....

Carlos E. Alchourron, Peter Gardenfors and David Makinson. On the the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50: 510--533, 1985.

....example that will give the same proof. xiv EYAL AMIR 5 RELATION TO BELIEF REVISION AND ILP A close issue to our presentation of Elaboration Tolerance is Belief Revision. Belief Revision is the process that a logical theory T goes through when we wish to incorporate some new information (see [ Alchourr on et al. 1985 ] Katsuno and Mendelzon, 1991 ] Lehmann, 1995 ] Antoniou, 1997 ] The main di erence between the work done on Belief Revision and the Elaboration Tolerance treatment we presented here is that the latter is interested in the sequence of actions (e.g. syntactic additions to the ....

Carlos E. Alchourron, Peter Gardenfors, and David Makinson. On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50:510-530, 1985.

....more information than is possessed by either of its two arguments, di usion produces a state with less information. Fusion and di usion are symmetric operators, and together de ne a distributive lattice. 1 Introduction In what is by now classical work, Alchourr on, G ardenfors, and Makinson [14, 2] proposed a theory of reasonable belief revision, the AGM theory henceforth. The intention of the theory is to formalize an Occam s razor principle, ensuring that beliefs change only when forced to by new information. The most common way of presenting the AGM theory is through the famous AGM ....

Carlos E. Alchourron, Peter Gardenfors, and David Makinson. On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50:510-530, 1985.

.... Intelligence, e.g. in updating logical database [ Fagin et al. 1983 ] in hypothetical reasoning [ Ginsberg, 1986 ] and in machine learning [ Wrobel, 1994 ] Most of the research in this area is influenced by work in philosophical logic, in particular by Gardenfors and his colleagues [ Alchourr on et al. 1985; Gardenfors, 1988; Gardenfors, 1992a ] who developed the theory of belief revision. Here we will focus on the computational aspects of this theory, surveying results that address the issue of the computational complexity of belief revision. The theory of belief revision gives a quite accurate ....

....with the conjunction of all formulae V C. If S = fA 1 ; A n g is a finite family of finite belief bases, then W S shall denote a formula logically equivalent to ( V A 1 ) V A n ) As usual, we set W ; 2. 2 Rationality Postulates Gardenfors and his colleagues [ Alchourr on et al. 1985; Gardenfors, 1988 ] considered mainly two change operations on belief sets, namely, contraction and revision. Contraction is the removal of a formula from a belief set K resulting in a new belief set, denoted by K : Gamma , that does not contain (if is not a tautology) and revision is ....

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Carlos E. Alchourr'on, Peter Gardenfors, and David Makinson. On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50(2):510--530, June 1985.

....having a different class of hypotheses (predicate calculus Horn theories, rather than propositional conjunctions) More significantly, we present situations where the computational task is not just intractable, but is not even approximatable. Like theory revision systems, belief revision systems [1, 13, 23, 31] also modify a given theory to incorporate some new observations about the world. Such formalisms take as input an initial theory T 0 and a new assertion hq; i, resp. new retraction hr; Gammai) and return a new (consistent) theory T 0 that entails q (resp. does not entail r) but otherwise ....

Carlos E. Alchourr'on, Peter Gardenfors, and David Makinson. On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50:510--530, 1985.

....The notion of revision adopted will determine which conditionals are accepted and rejected. Conversely, given a fixed (complete) set of accepted conditionals, the revision function adopted by an agent will also be determined. The AGM theory of revision due to Alchourr on, G ardenfors and Makinson [2] provides guidelines for the revision of objective belief sets (containing no conditional sentences) These are usually presented as postulates that constrain the behavior of revision functions. We use K A to denote the To appear, Journal of Philosophical Logic, 1995 1 INTRODUCTION 2 belief ....

....if K = Cn(S) for some finite set of premises S. The expansion of K by new information A is the belief set K A = Cn(K [ fAg) The revision of K by A is denoted K A . The process of revision requires some care, for A may contradict elements of K. Alchourr on, G ardenfors and Makinson [2] propose a method for logically delimiting the scope of acceptable revisions. To this end, the AGM postulates below, are maintained to hold for any reasonable notion of revision [15] R1) K A is a belief set (i.e. deductively closed) R2) A 2 K A . R3) K A K A . R4) If :A ....

Carlos Alchourr on, Peter G ardenfors, and David Makinson. On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50:510--530, 1985.

....of this meta level logic can provide a formal basis for requirements evolution. Specifically, our framework views a requirements model as a theory of some nonmonotonic logic, while requirements evolution involves mapping one such theory to another. We argue that the AGM theory of belief change [1] should provide the formal basis for the theory change component. We demonstrate our ideas by using the THEORIST system for nonmonotonic reasoning. As a demonstration of the utility of our framework, we analyze operators in the Telos system for requirements modeling to identify some obvious ....

....our default based framework and point out some obvious shortcomings of these operators. This serves to motivate the development of a new set of operators which may serve as the formal basis for requirements evolution. We apply belief revision techniques, as formalized in the so called AGM theory [1] [4] to define operations through which new requirements may be added or existing requirements may be retracted from a default based representation of a requirements model. We show how this new approach avoids the problems we identify with the operators in the Telos framework. This work thus ....

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Carlos E. Alchourr'on, Peter Gardenfors, and David Makinson. On the logic of theory change: partial meet contraction and revision functions. Journal of Symbolic Logic, 50:510--530, 1985.

....in a principled, systematic manner. The principle of minimal change (minimality principle) is one of the principles used to carry out such systematic model elimination. The minimality principle manifests in different forms in different approaches to reasoning. In the belief revision framework [Gar88, AGM85], the reasoner, after receiving the evidence, entertains as serious possibilities only those models that are, among the models that satisfy the evidence, minimally different distant from the set of currently flier tweety nonflier tweety nonbird tweety bird tweety Figure 1: model elimination in ....

Carlos E. Alchourron, Peter Gardenfors, and David Makinson. On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50:510--530, 1985.

....associated with access and augmentation. Hence, we may conclude that belief revision is a phenomenon not analyzable on the knowledge level. However, the theory of epistemic change and the logic of theory change developed by Alchourr on, Gardenfors, and Makinson [ Alchourr on and Makinson, 1982; Alchourr on et al. 1985; Makinson, 1985; Makinson, 1987; Gardenfors, 1988; Gardenfors, 1989 ] which will be described briefly in Section 2, show that at least some aspects of belief revision can be subject to a knowledge level analysis. Based on some rationality postulates any epistemic change operation should ....

....: Gamma x (5) Turning now to revision, we note that there are two independent ways to characterize this operation. First, a set of rationality postulates for revision could be specified capturing the idea that a revised belief set should minimally differ from the original belief set, as done in [ Alchourr on et al. 1985 ] Second, one could define the revision operation A : x by first contracting A with respect to :x in order to avoid inconsistencies, and then expanding the result by x: A : x def = A : Gamma :x) x (6) 2 Proofs for the principles (4) and (5) can be found in [G ardenfors, 1988] ....

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Carlos E. Alchourr'on, Peter Gardenfors, and David Makinson. On the Logic of Theory Change: Partial Meet Contraction and Revision Functions. The Journal of Symbolic Logic 50(2): 510--530, June 1985.

....Belief revision and belief update are two of the most important types of belief change. Although similar in some ways, these two processes are believed to be fundamentally different. In this paper we take a closer look at belief revision (as formalized by Alchourron, Gardenfors and Makinson [1]) and belief update (as modelled by Katsuno and Mendelzon [4] The results we obtain herein show that the two processes differ, not so much in the way they change a fixed belief state K , but rather on how changes at different theories are related to each other. 1 Introduction Two of the most ....

....belief revision and belief update (or revision and update for short) Belief revision is the process by which a rational agent changes her beliefs about a static world in the light of new information. Much of the research in the field is based on the work of Alchourron, Gardenfors, and Makinson [1] who have developed a framework, which we call the AGM paradigm, for studying this process. In the AGM paradigm belief revision is modelled as a function over logical theories, called a revision function, which satisfies a set of rationality postulates (known as the AGM postulates) Belief ....

Carlos E. Alchourron, Peter Gardenfors, and David Makinson, `On the logic of theory change: Partial meet contraction and revision functions', The Journal of Symbolic Logic, 50(2), 510--530, (1985).

....are denoted and , respectively. 2.1 The AGM Model The expansion of K by new information A is the belief set K A = Cn(K [ fAg) The revision of K by A is denoted K A . The process of revision requires some care, for A may contradict elements of K. Alchourr on, Gardenfors and Makinson [2] propose a method for logically delimiting the scope of acceptable revisions. To this end, the AGM postulates below, are maintained to hold for any reasonable notion of revision [12] R1) K A is a belief set (i.e. deductively closed) R2) A 2 K A . R3) K A K A . R4) If :A ....

Carlos Alchourr'on, Peter Gardenfors, and David Makinson. On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50:510--530, 1985.

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Carlos Alchourron, Peter Gardenfors, and David Makinson. On the Logic of Theory Change: Partial Meet Contraction and Revision Functions. The Journal of Symbolic Logic, 50:510--530, 1985.

No context found.

Carlos E. Alchourr'on, Peter Gardenfors, and David Makinson. On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50(2):510--530, June 1985.

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Carlos E. Alchourr'on, Peter Gardenfors, and David Makinson. On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50(2):510--530, June 1985.

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Carlos Alchourr'on, Peter Gardenfors, and David Makinson. On the logic of theory change: Partial meet contraction and revision functions. J. of Symbolic Logic, 50:510--530, 1985.

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