GABBAY, D., AND PH.SMETS, Eds. Handbook on Defeasible Reasoning and Uncertainty Management Systems, vol. III: Belief Change. Kluwer Academic, 1998.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... classical model theoretic entailment under preferential structures [51, 34] infinitesimal probabilities [1, 47] possibility measures [17] and world rankings [52, 31] They also characterize an entailment relation based on conditional objects [18] A survey of all these relationships is given in [6, 24]. Mainly to solve problems with irrelevant information, the notion of rational closure as a more adventurous notion of entailment was introduced by Lehmann [36, 38] It is equivalent to entailment in System by Pearl [48] to the least specific possibility entailment by Benferhat et al. 5] ....

D. M. Gabbay and P. Smets, editors. Handbook on Defeasible Reasoning and Uncertainty Management Systems. Kluwer Academic, Dordrecht, Netherlands, 1998.

.... preferential structures [SHO 87, KRA 90] infinitesimal probabilities [ADA 75, PEA 89] possibility measures [DUB 91] and world rankings [SPO 88, GOL 92] They also characterize an entailment relation based on conditional objects [DUB 94] A survey of all these relationships is given in [BEN 97, GAB 98] In this paper, we show that probabilistic reasoning under coherence is reducible to model theoretic probabilistic reasoning using concepts from default reasoning. Crucially, we even show that probabilistic reasoning under coherence is a generalization of . That is, we give a new probabilistic ....

....next theorem shows that g coherence has a characterization similar to the one consistency in default reasoning by Goldszmidt and Pearl [GOL 91] It follows from Theorem 3.2. To formulate this result, we adopt the following terminology from default reasoning from conditional knowledge bases [GAB 98, BEN 97] A probabilistic interpretation verifies a conditional constraint j L IF HJ YH # : a . A set of conditional constraints tolerates a conditional constraint under a set of logical constraints iff there exists a model of that verifies . is under iff ....

GABBAY D. M., SMETS P., Eds., Handbook on Defeasible Reasoning and Uncertainty Management Systems, Kluwer Academic, Dordrecht, Netherlands, 1998.

.... probabilistic reasoning # Can algorithms that have been developed for efficient reasoning in one area also be used in the other area Interestingly, it turns out that the answers to these two questions are closely related to the area of default reasoning from conditional knowledge bases [19]. Roughly speaking, coherence based probabilistic reasoning can be understood as a combination of model theoretic probabilistic logic with concepts from default reasoning. That is, deciding coherence and computing tight intervals under coherence can be reduced to standard reasoning tasks in ....

....Logic We now recall some of our results obtained in [3] which concern characterizations of the notions of g coherence and of g coherent entailment in terms of the notions of satisfiability and of logical entailment. We adopt the following terminology from the area of default reasoning [19]. A probabilistic interpretation verifies . A set of conditional constraints # tolerates under a set of logical constraints iff there exists a model of # that verifies . The following theorem shows that g coherence has a characterization similar to consistency in default ....

D. M. Gabbay and P. Smets, editors. Handbook on Defeasible Reasoning and Uncertainty Management Systems. Kluwer Academic, Dordrecht, Netherlands, 1998.

.... classical model theoretic entailment under preferential structures [58, 41] infinitesimal probabilities [1, 54] possibility measures [19] and world rankings [59, 36] They also characterize an entailment relation based on conditional objects [20] A survey of all these relationships is given in [6, 26]. Mainly to solve problems with irrelevant information, the notion of rational closure as a more adventurous notion of entailment was introduced by Lehmann [43, 45] It is equivalent to entailment in System by Pearl [55] to the least specific possibility entailment by Benferhat et al. 5] and ....

D. M. Gabbay and P. Smets, editors. Handbook on Defeasible Reasoning and Uncertainty Management Systems. Kluwer Academic, Dordrecht, Netherlands, 1998.

....equivalences are not incidental is shown by Friedman and Halpern [22] who prove that many approaches are expressible as plausibility measures and thus they must, under some weak natural conditions, inevitably amount to the same notion of inference. A survey of the above relationships is given in [5, 24]. Mainly to solve problems with irrelevant information, the notion of rational closure as a more adventurous notion of entailment was introduced by Lehmann [38, 40] It is equivalent to entailment in System by Pearl [50] to the least specific possibility entailment by Benferhat et al. 4] and ....

D. M. Gabbay and P. Smets, editors. Handbook on Defeasible Reasoning and Uncertainty Management Systems. Kluwer Academic, Dordrecht, Netherlands, 1998.

..... 40 1 Introduction Updating knowledge bases is an important issue in the area of data and knowledge representation. While this issue has been studied extensively in the context of classical knowledge bases (cf. e.g. [32, 19]) attention to it in the area of nonmonotonic knowledge bases, in particular in logic programming, is more recent. Various approaches to evaluating logic programs in the light of new information have been presented. The proposals range from basic methods to incorporate an update U , given by a ....

D. Gabbay and P. Smets, editors. Handbook on Defeasible Reasoning and Uncertainty Management Systems, volume III: Belief Change. Kluwer Academic, 1998.

....been extensive work on laying the foundations of inference systems for plausible reasoning in the presence of incomplete information. In particular, characterizing natural properties of such systems and their inference relations embodied was a major subject of study in nonmonotonic reasoning (cf. [37, 38]) Conditional knowledge bases. A conditional knowledge base consists of a collection of strict statements in classical logic and a collection of defeasible rules (also called defaults) The former are statements that must always hold, while the latter are rules that read as generally, if ....

D. M. Gabbay and P. Smets, editors. Handbook on Defeasible Reasoning and Uncertainty Management Systems. Kluwer Academic, Dordrecht, Netherlands, 1998.

....of processing general first order queries is not considered. In section 4, we describe how the approach of Kifer and Lozinskii [50] can be adapted to the task of computing consistent query answers. Related treatments of inconsistency have been developed in the areas of knowledge representation [32], and formal specifications in software engineering [11, 67] 7.3 Databases Asirelli et al. 10] treat ICs as views over a deductive database. In that way, queries can be answered through the views , in such a way that the resulting answers satisfy the ICs, and answers that do not satisfy them ....

Gabbay, D. and Smets, P. (eds.) Handbook of Defeasible Reasoning and Uncertainty Management Systems, Vols. 1 & 2, Kluwer, 1998.

.... classical model theoretic entailment under preferential structures [38, 25] infinitesimal probabilities [1, 34] possibility measures [12] and world rankings [40, 24] They also characterize an entailment relation based on conditional objects [13] A survey of all these relationships is given in [3, 16]. In this paper, we show that probabilistic reasoning under coherence is reducible to model theoretic probabilistic reasoning using concepts from default reasoning. Crucially, we even show that probabilistic reasoning under coherence is a generalization of default reasoning in System . That is, ....

....The next theorem shows that g coherence has a characterization similar to the one of consistency in default reasoning by Goldszmidt and Pearl [23] It follows from Theorem 3.2. To formulate this result, we adopt the following terminology from default reasoning from conditional knowledge bases [16, 3]. A probabilistic interpretation verifies a conditional constraint : # E GH OGY : A set of conditional constraints tolerates a conditional constraint there exists a model of that verifies . We say is under iff no model of . is g coherent iff there ....

D. M. Gabbay and P. Smets, editors. Handbook on Defeasible Reasoning and Uncertainty Management Systems. Kluwer Academic, Dordrecht, Netherlands, 1998.

.... classical model theoretic entailment under preferential structures [50, 34] infinitesimal probabilities [1, 46] possibility measures [17] and world rankings [51, 31] They also characterize an entailment relation based on conditional objects [18] A survey of all these relationships is given in [6, 24]. Mainly to solve problems with irrelevant information, the notion of rational closure as a more adventurous notion of entailment was introduced by Lehmann [36, 38] It is equivalent to entailment in System Z by Pearl [47] to the least specific possibility entailment by Benferhat et al. 5] and ....

D. M. Gabbay and P. Smets, editors. Handbook on Defeasible Reasoning and Uncertainty Management Systems. Kluwer Academic, Dordrecht, Netherlands, 1998.

....finitary characterizations of the evolution, and derive complexity results for our framework. 1 Introduction Updating knowledge bases is an important issue in the area of data and knowledge representation. While this issue has been studied extensively in the context of classical knowledge bases [18, 11], attention to it in the area of nonmonotonic knowledge bases, in particular in logic programming, is more recent. Various approaches to evaluating logic programs in the light of new information have been presented, cf. 1] The proposals range from basic methods to incorporate an update U , given ....

D. Gabbay and P. Smets, editors. Handbook on Defeasible Reasoning and Uncertainty Management Systems, Vol. III. Kluwer Academic, 1998.

.... classical model theoretic entailment under preferential structures [34, 24] infinitesimal probabilities [1, 31] possibility measures [12] and world rankings [36, 23] They also characterize an entailment relation based on conditional objects [13] A survey of all these relationships is given in [3, 16]. In this paper, we show that probabilistic reasoning under coherence is reducible to model theoretic probabilistic reasoning using concepts from default reasoning. Crucially, we even show that probabilistic reasoning under coherence is a generalization of default reasoning in System P . That is, ....

..... The next theorem shows that g coherence has a characterization similar to the one of p consistency in default reasoning by Goldszmidt and Pearl [22] It follows from Theorem 3.2. To formulate this result, we adopt the following terminology from default reasoning from conditional knowledge bases [16, 3]. A probabilistic interpretation Pr verifies a conditional constraint ( j ) l; u] iff Pr( 0 and Pr j= j ) l; u] A set of conditional constraints P tolerates a conditional constraint F under a set of logical constraints L iff there exists a model of L[P that verifies F . We say P is under L in ....

D. M. Gabbay and P. Smets, editors. Handbook on Defeasible Reasoning and Uncertainty Management Systems. Kluwer Academic, Dordrecht, Netherlands, 1998.

....be expressed by a defeasible rule (as penguins are birds that do not fly) The semantics of a conditional knowledge base is given by the set of all plausibly entailed defaults. Several different semantics for conditional knowledge bases have been proposed in the literature (see the surveys in [23, 71, 30]) The desired behavior has been characterized by benchmark examples and by general nonmonotonic properties. 2.2.2. Benchmark Examples We now describe some important benchmark examples for default reasoning from conditional knowledge bases. These examples show the close relationship between ....

....Default Reasoning with Conditional Constraints 23 bases. We then show that the new formalisms have a very nice behavior in our benchmark examples. 5.1. PRELIMINARIES We start by defining the probabilistic counterparts of some important concepts from classical default reasoning (see the surveys in [23, 71, 30]) A probabilistic interpretation V verifies a default Oo n qQ 4 iff ROP rQ and R = Oo rQ 0 . We say R falsifies a default Oo rQ 0 iff ROP rQ = and VS6 = Oo rQ 4 . A set of defaults tolerates a default under a set of strict logical ....

Gabbay, D. M. and P. Smets (eds.): 1998, Handbook on Defeasible Reasoning and Uncertainty Management Systems. Dordrecht, Netherlands: Kluwer Academic.

.... probabilistic reasoning Can algorithms that have been developed for efficient reasoning in one area also be used in the other area Interestingly, it turns out that the answers to these two questions are closely related to the area of default reasoning from conditional knowledge bases [19]. Roughly speaking, coherence based probabilistic reasoning can be understood as a combination of model theoretic probabilistic logic with concepts from default reasoning. That is, deciding coherence and computing tight intervals under coherence can be reduced to standard reasoning tasks in ....

....Logic We now recall some of our results obtained in [3] which concern characterizations of the notions of g coherence and of g coherent entailment in terms of the notions of satisfiability and of logical entailment. We adopt the following terminology from the area of default reasoning [19]. A probabilistic interpretation Pr verifies a conditional constraint ( j ) l; u] iff Pr( 0 and Pr j= j ) l; u] A set of conditional constraints P tolerates a conditional constraint F under a set of logical constraints L iff there exists a model of L[P that verifies F . The following ....

D. M. Gabbay and P. Smets, editors. Handbook on Defeasible Reasoning and Uncertainty Management Systems. Kluwer Academic, Dordrecht, Netherlands, 1998.

.... INFSYS RR 1843 01 04 3 Can algorithms that have been developed for efficient reasoning in one area also be used in the other area Interestingly, it turns out that the answers to these two questions are closely related to the area of default reasoning from conditional knowledge bases [18]. Roughly speaking, coherence based probabilistic reasoning can be understood as a combination of model theoretic probabilistic logic with concepts from default reasoning. That is, deciding coherence and computing tight intervals under coherence can be reduced to standard reasoning tasks in ....

....Logic We now recall some of our results obtained in [3] which concern characterizations of the notions of gcoherence and of g coherent entailment in terms of the notions of satisfiability and of logical entailment. We adopt the following terminology from the area of default reasoning [18]. A probabilistic interpretation Pr verifies a conditional constraint ( j ) l; u] iff Pr( 0 and Pr j= j ) l; u] A set of conditional constraints P tolerates a conditional constraint F under a set of logical constraints L iff there exists a model of L[P that verifies F . The following ....

D. M. Gabbay and P. Smets, editors. Handbook on Defeasible Reasoning and Uncertainty Management Systems. Kluwer Academic, Dordrecht, Netherlands, 1998.

.... classical model theoretic entailment under preferential structures [32, 23] infinitesimal probabilities [1, 29] possibility measures [12] and world rankings [34, 22] They also characterize an entailment relation based on conditional objects [13] A survey of all these relationships is given in [3, 16]. Roughly speaking, coherence based probabilistic reasoning can be reduced to model theoretic probabilistic reasoning using concepts from default reasoning. Crucially, it even turns out that coherence based probabilistic reasoning is a probabilistic generalization of default reasoning in system ....

.... P , there exists a model Pr of L[P n such that Pr( 1 n ) 0 . It then follows that g coherence has a characterization similar to p consistency in default reasoning. To formulate this result, we adopt the following terminology from default reasoning from conditional knowledge bases [16, 3]. A probabilistic interpretation Pr verifies a conditional constraint ( j ) l; u] iff Pr( 0 and Pr j= j ) l; u] A set of conditional constraints P tolerates a conditional constraint F under a set of logical constraints L, iff there exists a model of L[P that verifies F . We say P is under ....

D. M. Gabbay and P. Smets, editors. Handbook on Defeasible Reasoning and Uncertainty Management Systems. Kluwer Academic, Dordrecht, Netherlands, 1998.

....be expressed by a defeasible rule (as penguins are birds that do not fly) The semantics of a conditional knowledge base is given by the set of all plausibly entailed defaults. Several different semantics for conditional knowledge bases have been proposed in the literature (see the surveys in [19, 66, 26]) The desired behavior has been characterized by benchmark examples and by general nonmonotonic properties. 2.2.2 Benchmark Examples We now describe some important benchmark examples for default reasoning from conditional knowledge bases. These examples show the close relationship between ....

....default theories and knowledge bases. We then show that the new formalisms have a very nice behavior in our benchmark examples. 5. 1 Preliminaries We start by defining the probabilistic counterparts of some important concepts from classical default reasoning (see especially the surveys in [19, 66, 26]) INFSYS RR 1843 00 02 17 Table 3: Tight conclusions under naive probabilistic default reasoning and reference class reasoning. k 0 tight k 1 tight T KB ( j ) k rc tight k dF 0 tight k dF 1 tight (1) T 1 (bird j ) 1; 1] legsj ) 95; 1] 95; 1] 95; 1] 2) T 1 (bird ....

D. M. Gabbay and P. Smets, editors. Handbook on Defeasible Reasoning and Uncertainty Management Systems. Kluwer Academic, Dordrecht, Netherlands, 1998.

....been extensive work on laying the foundations of inference systems for plausible reasoning in the presence of incomplete information. In particular, characterizing natural properties of such systems and their inference relations embodied was a major subject of study in nonmonotonic reasoning (cf. [37, 38]) Conditional knowledge bases. A conditional knowledge base consists of a collection of strict statements in classical logic and a collection of defeasible rules (also called defaults) The former are statements that must always hold, while the latter are rules that read as generally, if ....

D. M. Gabbay and P. Smets, editors. Handbook on Defeasible Reasoning and Uncertainty Management Systems. Kluwer Academic, Dordrecht, Netherlands, 1998.

....been extensive work on laying the foundations of inference systems for plausible reasoning in the presence of incomplete information. In particular, characterizing natural properties of such systems and their inference relations embodied was a major subject of study in nonmonotonic reasoning (cf. [23, 24]) A conditional knowledge base consists of a collection of strict statements in classical logic and a collection of defeasible rules (also called defaults) The former are statements that must always hold, while the latter are rules that read as generally, if then . Such rules may have ....

D. M. Gabbay and P. Smets, editors. Handbook on Defeasible Reasoning and Uncertainty Management Systems. Kluwer Academic, Dordrecht, Netherlands, 1998.

No context found.

Gabbay, D. M., & Smets, P. (Eds.). (1998). Handbook of defeasible reasoning and uncertainty management systems. Kluwer, Doordrecht, The Netherlands.

....the class and the attributes are represented by fuzzy values. Fuzziness that occurs in classes and attributes are not considered in this paper, but the technique developed here could be extended to such types of data. The belief function theory, as understood in the Transferable Belief Model [35] [37], provides a very powerful tool to deal with epistemic uncertainty. It provides a mathematical tool to treat subjective, personal judgments on the di#erent parameters of any classification problem and can be easily extended to deal with objective probabilities. It allows experts to express partial ....

....this quantity cannot be apportioned to any strict subset of A. So, it represents the specific support given to A. 5 Shafer [26] has initially proposed a normality condition expressed by: m(#) 0 (8) A bba that satisfies (8) is called a normalized basic belief assignment function. Smets [32, 37] relaxes this condition and interprets m(#) as the part of belief given to the fact that none of the hypotheses in # is true or as the amount of conflict between the pieces of evidence. The subsets A of the frame of discernment # such that m(A) is strictly positive, are called the focal elements ....

P. Smets, Numerical representation of uncertainty, D. M. Gabbay and Ph. Smets (eds.), Handbook of Defeasible Reasoning and Uncertainty Management Systems, Vol. 3, pp 265-309, Klower Academic Publishers, 1998.

....of the Intern. J. Approx. # This work has been partially funded by the CEC ESPRIT IV Working Group FUSION (project 20001) for both authors, by by the Communaute Francaise de Belgique, ARC 92 97160 (BELON) for the second author. 1 Reasoning, vol. 4, 1990 and vol. 6, 1992, Smets, 1994) and (Gabbay Smets, 1998)) This article proposes an interpretation of belief functions in terms of selfconditional expected probabilities . Dempster s original idea was that belief functions reflect constraints on belief states (i.e. probabilities) induced by partial knowledge of a special kind. This is reviewed in the ....

Gabbay, D. M., & Smets, P. (Eds.). (1998). Handbook of defeasible reasoning and uncertainty management systems. Kluwer, Doordrecht, The Netherlands.

No context found.

GABBAY, D., AND PH.SMETS, Eds. Handbook on Defeasible Reasoning and Uncertainty Management Systems, vol. III: Belief Change. Kluwer Academic, 1998.

No context found.

Dov M. Gabbay and Philippe Smets, editors. Handbook of Defeasible Reasoning and Uncertainty Management Systems Volume 3: Belief Change. Kluwer Academic Publishing, 1998.

No context found.

Gabbay, D. M. and P. Smets (eds.): 1998, Handbook on Defeasible Reasoning and Uncertainty Management Systems. Dordrecht, Netherlands: Kluwer Academic.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC