M.A. Williams. Iterated theory base change: A computational model. In Proc. of the 14th Inter. Joint Conf. on Artificial Intelligence, pages 1541--1547, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....here. Several proposals for formalisms that incorporate this ability have been made for the merging of structures in which it is possible to encode the preferences of sources. In [5, 4] information fusion is described in terms of possibility distributions [7] and the framework developed in [25]. In [16, 17] information merging is described in terms of epistemic states; structures in the style of [24] In [1] the combination of preferences is described in a framework where preferences are represented as arbitrary binary relations. In each of these frameworks, the notion of what would ....

....of L; the lower the number assigned to a valuation, the more plausible it is deemed to be. This is along the lines of work initially proposed by Spohn [24] and was used in [16, 17] to define merging. Epistemic states are very similar to possibility distributions [7] and the framework of Williams [25]; it is relatively easy to translate between these frameworks. It is possible to use epistemic states in various ways. In the context of merging our aim is to employ epistemic states semi qualitatively. The intention is for the ranks assigned to valuations to serve merely as markers in order to ....

Mary-Anne Williams. Iterated theory base change: a computational model. In IJCAI-95. Proceedings of the 14th International Joint Conference on Artificial Intelligence, volume 2, pages 1541--1547, San Francisco, CA, 1995. International Joint Conference on Artificial Intelligence, Morgan Kaufmann.

....revision operators with memory use the faithful assignment provided by the classical AGM revision operator as an a priori information. This a priori information is attached to the new evidence, and the completed information obtained is then incorporated see also [Spohn, 1987; Williams, 1994; Williams, 1995] . We do not adress this kind of operators in this paper since they require an additional numerical information with the new evidence. to the old epistemic state with the usual primacy of update requirement. The ontology for this pre processing step, associating an additional information to the ....

M. A. Williams. Iterated theory base change: a computational model. In Proceedings of the Fourteenth International Joint Conference on Arti cial Intelligence (IJCAI'95), pages 1541 { 1550, 1995.

....sources in a coherent and rational way. Recently, several proposals have been made for the merging of structures in which it is possible to encode the preferences of sources. In [5, 4] information fusion is described in terms of possibility distributions [7] and the framework developed in [21]. In [13, 14] information merging is described in terms of epistemic states; structures in the style of [20] In [1] the combination of preferences is described in a framework where preferences are represented as arbitrary binary relations. It has been pointed out that the merging of information ....

....; the lower the number assigned to a valuation, the more plausible it is deemed to be. This is along the lines of work initially proposed by Spohn [20] It was used in [13, 14] to define merging. Epistemic states are very similar to possibility distributions [7] and the framework of Williams [21] and it is relatively easy to translate between these frameworks. It is possible to use epistemic states in various ways. In the context of merging our aim is to employ epistemic states semi qualitatively. The intention is for the ranks assigned to valuations to serve merely as markers in order to ....

Mary-Anne Williams. Iterated theory base change: a computational model. In IJCAI-95. Proceedings of the 14th International Joint Conference on Artificial Intelligence, volume 2, pages 1541--1547, San Francisco, CA, 1995. International Joint Conference on Artificial Intelligence, Morgan Kaufmann.

....function based on the original theory, the input formula and the previous change function is speci ed. This can be done in a qualitative way as in [ Boutilier, 1996; Hansson, To come; Nayak, 1994; Lehmann, 1995 ] or by enriching the model with numbers [ Darwiche and Pearl, 1997; Spohn, 1987; Williams, 1995 ] Notice that in these approaches we are not really going back to a binary function and returning the theory K to its original role of argument. The construction method is more exible than considering a binary function. Given a theory K and a formula , change functions associated to K ....

M. Williams. Iterated theory base change: A computational model. In IJCAI-95 Proceeding of the 14th International Joint Conference on Articial Intelligence, pages 1541-1550. Morgan Kauman, 1995.

....be different from the one defined on K 3. the choice of a particular ordering satisfying the postulates EE1 Xi EE5 is arbitrary; as Gardenfors wrote: the postulates] leave the main problem unsolved: what is a reasonable metric for comparing different epistemic states . Mary Anne Williams [ 26 ] showed how the first two problems can be solved in theoretically satisfying ways wholely within the AGM paradigm . She pointed out that, belief revision means epistemic entrenchment revision : incoming information transmutes the old epistemic entrenchment into a new one which, in turn, yields ....

M.A. Williams. Iterated theory base change: A computational model. In Proc. of the 14th Inter. Joint Conf. on Artificial Intelligence, pages 1541--1547, 1995.

....= Cognitive State K Incoming Information A Revised Cognitive State K A Syntactic Connotation Semantic Connotation Fig 1. Syntactic and Semantic connotations of the Belief Revision process Most of the methods for belief revision developed so far obey the following three rationality principles [1,2,22 27]: BR1. Consistency: K A should be consistent (whatever it coud mean in a numerical setting) BR2. Minimal Change: K A should be as close as possible to K BR3. Priority of Incoming Information: K A must embody A (this is the reason why A comes without a weight in Figure 1; its weight is ....

Williams M.A. (1995), Iterated Theory Base Change: A Computational Model, in Proc. of the 14th Inter. Joint Conf. on Artificial Intelligence, pp. 1541-1547.

....Th(W ) But in practice W will be a finite axiomatization of the facts, thus we need to use operators which work on finite bases rather than deductively closed theories. More information on these issues, including the relationship between theory base revision and AGM belief revision are found in [16]. Theorem 1. a) If is not a contradiction, then T sc . b) If E is an extension of T such that 2 E, then E is an extension of T . 3.2 Revision Adding a Formula to At Least One Extension In this case we don t necessarily want to add to every extension. On the other hand, ....

M.A. Williams. Iterated Theory Base Change: A Computational Model. In Proc. 14th International Joint Conference on Artificial Intelligence, 1541-1550, Morgan Kaufmann 1995 .

....for a Multi Source environment ) Derived from researches in multi agent [1] and investigative domains [2] MSBR is a novel assembly of known techniques to the treatment of consistency and uncertainty. Let us recapitulate here the main ideas. Defined as a symbolic model theoretical problem [3 6], belief revision has also been approached both as a qualitative syntactic process [7,8] and as a numerical mathematical issue [9] Beliefs can be represented either as weighted sentences or as sets of weighted possible worlds (the models of the sentences) Weights can be either reals (normally ....

Williams M.A., Iterated Theory Base Change: A Computational Model, in Proc. of the 14th Inter. Joint Conf. on Artificial Intelligence, pp. 1541-1547, 1995.

....However the total pre orders associated with two succesive epistemic states are not related, the only requirement is that these pre orders are faithful. Iterated revision has been recently brought into focus by several authors, some proposing a framework for iterated revision like Williams [8] [9] with transmutations, Boutilier [2] with natural revision, Friedman and Halpern [4] with Belief Change Systems. Other approaches start with the AGM postulates and augment them in order to characterize iterated revision. Boutilier [2] opts for an absolute minimization strategy. Lehmann [6] ....

....by a pair ( m) where is a propositional formula and m is the post revision degree of plausibility of . Revising an epistemic state by a new observation, also called ( m) conditionalization, occurs changing the ranking of interpretations. Extending Spohn s work, M. A. Williams [8] [9] refers to the process of changing an underlying preference relation as a transmutation. The observation is a formula ff and an ordinal i which represents the information to be accepted with a degree of firmness i. The (ff; i) transmutation of a ranking involves minimal change to the initial ....

M. A. Williams. Iterated Theory Base Change:A Computational Model. In Proceedings of 14th Int. Joint Conf. on Artificial Intelligence, pages 1541--1547, 1995.

....section) the Bayesian Conditioning to perform O2 and the Assumption Based approach to perform O3. Starting from the beginning, let us recapitulate here our ideas about how to revise integrate beliefs in a multi agent environment. Initially defined as a symbolic model theoretical problem [3 6], belief revision has also been approached both as a qualitative syntactic process [7,8] and as a numerical mathematical issue [9] Beliefs can be represented either as weighted sentences of a decidable language L or as sets of weighted possible worlds (the models of the sentences) Weights can be ....

Williams M.A., Iterated Theory Base Change: A Computational Model, in Proc. of the 14th Inter. Joint Conf. on Artificial Intelligence, pp. 1541-1547, 1995.

.... the logical content of the beliefs but works with infinite sets of sentences C1.2 Revision as Transmutation of Partial Epistemic Rankings [12] seems to be computationally intractable C1.3 Revision for finite bases [3] the outcome depends on the syntax of the beliefs C2 Numerical approaches [10]: generally, they do not respect the logical content of the sentences C2.1 probabilistic approaches [14] do not deal with inconsistencies C2.2 possibilistic approaches [13] lead to a very drastic revision C2.3 evidence based approaches [15] are very computationally complex In all these ....

....that the kind and the importance of these emergent effects can be evaluated only on a simulation basis. 2. A model for belief revision in a multi agent environment Most of the symbolic and numerical models for belief revision developed so far obey the following three rationality principles [1,2,3,10]: R1. Consistency: revision must yield a consistent knowledge space P2. Minimal Change: revision should alter as less as possible the previous knowledge space P3. Priority to the Incoming Information: the revised knowledge space must embody the information that caused the revision While the last ....

Williams M.A. (1995), Iterated Theory Base Change: A Computational Model, in Proc. of the 14th Int. Joint Conf. on Artificial Intelligence, pp. 1541-1547.

.... works of G rdenfors et al. 1,2] ideas on belief revision have been progressively refined [10] and ameliorated toward normative, effective and quasi computable paradigms [4 6] Some of the main contributes have been the idea of revision as transmutation of partial epistemic rankings [18], revision for finite bases [13] the distinction between revision and updating [11] and a related approach based on the notion of possible models [3] Side by side to this symbolic line of research, there has been also a numerical way to belief revision [8] whose main contributes were the ....

....unsolved: what is a reasonable metric for comparing different epistemic states . Our Claim Regarding the last problem, the opinion implicitly expressed in this paper is that, practically, such computable and reasonable metric can be provided only by numerical approaches. Mary Anne Williams [18] showed how the first two problems can be solved in theoretically satisfying ways wholely within the AGM paradigm . She pointed out that, belief revision means epistemic entrenchment revision : incoming information transmutes the old epistemic entrenchment into a new one which, in turn, yields ....

WILLIAMS M.A. (1995), Iterated Theory Base Change: A Computational Model, in Proc. of the 14th Inter. Joint Conf. on Artificial Intelligence, pp. 1541-1547.

....be hard because knowledge is only partially explicit. Since the seminal, influential and philosophical work of Alchourr n, G rdenfors and Makinson [1] the ideas on belief revision have been progressively refined [2,3] and ameliorated toward normative, effective and quasi computable paradigms [4,5]. In this chapter, we begin by surveying some of the following contributes: 2 Symbolic approaches 2.1 Sentence based Revision 2.1.1 AGM Revision [1] respects the logical content of the beliefs but works with infinite sets of sentences 2.1.2 Revision as Transmutation of Partial Epistemic ....

....In this chapter, we begin by surveying some of the following contributes: 2 Symbolic approaches 2.1 Sentence based Revision 2.1.1 AGM Revision [1] respects the logical content of the beliefs but works with infinite sets of sentences 2.1. 2 Revision as Transmutation of Partial Epistemic Rankings [5]: seems to be computationally intractable 2.1.3 Revision for finite bases [4] the outcome depends on the syntax of the beliefs 2.2 Model Based Revision 2.2.1 KM Updating [6] 2.2.2 Possible Model Approach [7] 3 Numerical approaches [8] generally, they do not respect the logical content of the ....

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Williams, `Iterated Theory Base Change: A Computational Model', Proc. 14th Inter. Joint Conf. on Artificial Intelligence, (1995) 1541-1547.

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M-A. Williams. Iterated Theory Base Change: A Computational Model, in the Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence, Morgan Kaufmann Publishers, 1541 - 1550, 1995.

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Williams, M.A., Iterated Theory Base Change: A Computational Model, in the Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence, Morgan Kaufmann, 1541 -- 1550, 1995.

....entrenchment orderings of L where the elements of a finite (a not necessarily closed) set of sentences are mapped to the natural numbers. Definition: A finite partial entrenchment ranking is a function B from a finite subset of sentences in L into the 1 Partial entrenchments were defined in [Williams 1995], and essentially identical representations can be found in [Dubios et al. 1994, Rott 1992, Williams 1992] and elsewhere. natural numbers N such that the following conditions are satisfied for all ff 2 dom(B) PER1) If 6 ff then ffi 2 dom(B) B(ff) B(fi)g 6 ff. PER2) If :ff then B(ff) ....

....ff . The change functions defined above by maxiadjustment may not be the same as those obtained via Gardenfors and Makinson s construction using the epistemic entrenchment ordering derived in the obvious way from the relative ordering given by B using the function degree. Ordinary adjustment [Williams 1995] is a procedure that complies exactly with the standard entrenchment construction. There exist several variants of maxi adjustment, all are minor variations of the main algorithm described in the next section. Our implementation [Williams and Williams, 1997] offers anytime algorithms for all of ....

Williams, M.A. [1995] Iterated Theory Base Change: A Computational Model, IJCAI-95, Morgan Kaufmann, 1541 -- 1550.

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Williams, M.A., Iterated Theory Base Change: A Computational Model, in the Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence, 1995 (this volume).

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M.A. Williams. Iterated theory base change: A computational model. In Proc. of the 14th Inter. Joint Conf. on Artificial Intelligence, pages 1541--1547, 1995.

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M.-A. Williams. Iterated theory base change: A computational model. In Proceedings of the International Joint Conference on Artificial Intelligence, pages 1541--1547, Montreal, 1995. 42

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M-A. Williams. Iterated theory base change: A computational model. In C. S. Mellish, editor, Proc. of IJCAI'95, the 14th International Joint Conference on Articial Intelligence, pages 15411547, San Francisco, USA, 1995.

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M.-A. Williams. Iterated theory base change: A computational model. In Proceedings of the International Joint Conference on Artificial Intelligence, pages 1541--1547, Montr eal, 1995.

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Williams, `Iterated Theory Base Change: A Computational Model', Proc. 14th Inter. Joint Conf. on Artificial Intelligence, (1995) 1541-1547.

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M. A. Williams, Iterated theory base change: a computational model, In Proc. 14th Int. Joint Conf. on Artificial Intelligence (IJCAI'95),1541-1547, 1995.

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M. A. Williams, Iterated theory base change: a computational model, In Proc. 14th Int. Joint Conf. on Artificial Intelligence (IJCAI'95),1541-1547, 1995.

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Williams M. A., Iterated theory base change: a computational model, Proceedings of IJCAI- 95, 1995, 1541-1547.

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