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Representing Default Rules in Possibilistic Logic
, 1992
"... A key issue when reasoning with default rules is how to order them so as to derive plausible conclusions according to the more specific rules applicable to the situation under concern, to make sure that default rules are not systematically inhibited by more general rules, and to cope with the proble ..."
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Cited by 97 (36 self)
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A key issue when reasoning with default rules is how to order them so as to derive plausible conclusions according to the more specific rules applicable to the situation under concern, to make sure that default rules are not systematically inhibited by more general rules, and to cope with the problem of irrelevance of facts with respect to exceptions. Pearl's system Z enables us to rankorder default rules. In this paper we show how to encode such a rankordered set of defaults in possibilistic logic. We can thus take advantage of the deductive machinery available in possibilistic logic. We point out that the notion of inconsistency tolerant inference in possibilistic logic corresponds to the bold inference ; 1 in system Z. We also show how to express defaults by means of qualitative possibility relations. Improvements to the ordering provided by system Z are also proposed.
Nonmonotonic Reasoning, Conditional Objects and Possibility Theory
 Artificial Intelligence
, 1997
"... . This short paper relates the conditional objectbased and possibility theorybased approaches for reasoning with conditional statements pervaded with exceptions, to other methods in nonmonotonic reasoning which have been independently proposed: namely, Lehmann's preferential and rational closure en ..."
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Cited by 68 (17 self)
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. This short paper relates the conditional objectbased and possibility theorybased approaches for reasoning with conditional statements pervaded with exceptions, to other methods in nonmonotonic reasoning which have been independently proposed: namely, Lehmann's preferential and rational closure entailments which obey normative postulates, the infinitesimal probability approach, and the conditional (modal) logicsbased approach. All these methods are shown to be equivalent with respect to their capabilities for reasoning with conditional knowledge although they are based on different modeling frameworks. It thus provides a unified understanding of nonmonotonic consequence relations. More particularly, conditional objects, a purely qualitative counterpart to conditional probabilities, offer a very simple semantics, based on a 3valued calculus, for the preferential entailment, while in the purely ordinal setting of possibility theory both the preferential and the rational closure entai...
Belief Functions and Default Reasoning
, 2000
"... We present a new approach to deal with default information based on the theory of belief functions. Our semantic structures, inspired by Adams' epsilon semantics, are epsilonbelief assignments, where mass values are either close to 0 or close to 1. In the first part of this paper, we show that t ..."
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Cited by 38 (3 self)
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We present a new approach to deal with default information based on the theory of belief functions. Our semantic structures, inspired by Adams' epsilon semantics, are epsilonbelief assignments, where mass values are either close to 0 or close to 1. In the first part of this paper, we show that these structures can be used to give a uniform semantics to several popular nonmonotonic systems, including Kraus, Lehmann and Magidor's system P, Pearl's system Z, Brewka's preferred subtheories, Geffner's conditional entailment, Pinkas' penalty logic, possibilistic logic and the lexicographic approach. In the second part, we use epsilonbelief assignments to build a new system, called LCD, and show that this system correctly addresses the wellknown problems of specificity, irrelevance, blocking of inheritance, ambiguity, and redundancy.
Conditional Objects as Nonmonotonic Consequence Relationships
 IEEE Trans. Syst. Man Cybern
"... This paper is an investigation of the relationship between conditional objects obtained as a qualitative counterpart to conditional probabilities, and nonmonotonic reasoning. Roughly speaking, a conditional object can be seen as a generic rule which allows us to get a conclusion provided that the av ..."
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Cited by 37 (9 self)
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This paper is an investigation of the relationship between conditional objects obtained as a qualitative counterpart to conditional probabilities, and nonmonotonic reasoning. Roughly speaking, a conditional object can be seen as a generic rule which allows us to get a conclusion provided that the available information exactly corresponds to the "context" part of the conditional object. This gives freedom for possibly retracting previous conclusions when the available information becomes more specific. Viewed as an inference rule expressing a contextual belief, the conditional object is shown to possess all properties of a wellbehaved nonmonotonic consequence relation when a suitable choice of connectives and deduction operation is made. Using previous results from Adams' conditional probabilistic logic, a logic of conditional objects is proposed. Its axioms and inference rules are those of preferential reasoning logic of Lehmann and colleagues. But the semantics relies on a threevalu...
A preferencebased approach to default reasoning
, 1994
"... An approach to nonmonotonic inference, based on preference orderings between possible worlds or states of affairs, is presented. We begin with an extant weak theory of default conditionals; using this theory, orderings on worlds are derived. The idea is that if a conditional such as “birds fly ” is ..."
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Cited by 8 (0 self)
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An approach to nonmonotonic inference, based on preference orderings between possible worlds or states of affairs, is presented. We begin with an extant weak theory of default conditionals; using this theory, orderings on worlds are derived. The idea is that if a conditional such as “birds fly ” is true then, all other things being equal, worlds in which birds fly are preferred over those where they don’t. In this case, a red bird would fly by virtue of redbirdworlds being among the least exceptional worlds in which birds fly. In this approach, irrelevant properties are correctly handled, as is specificity, reasoning within exceptional circumstances, and inheritance reasoning. A sound prooftheoretic characterisation is also given. Lastly, the approach is shown to subsume that of conditional entailment.
Possibilistic Reasoning  A Minisurvey and Uniform Semantics
 Artificial Intelligence
, 1996
"... In this paper, we survey some quantitative and qualitative approaches to uncertainty management based on possibility theory and present a logical framework to integrate them. The semantics of the logic is based on the Dempster's rule of conditioning for possibility theory. It is then shown that clas ..."
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Cited by 5 (0 self)
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In this paper, we survey some quantitative and qualitative approaches to uncertainty management based on possibility theory and present a logical framework to integrate them. The semantics of the logic is based on the Dempster's rule of conditioning for possibility theory. It is then shown that classical modal logic, conditional logic, possibilistic logic, quantitative modal logic and qualitative possibilistic logic are all sublogics of the present logical framework. In this way, we can formalize and generalize some wellknown results about possibilistic reasoning in a uniform semantics. Moreover, our uniform framework is applicable to nonmonotonic reasoning, approximate consequence relation formulation, and partial consistency handling. Key words: Nonclassical logics, possibility theory, conditional possibility, modal logic, conditional logic. 1 Introduction There are essentially two kinds of logical formalisms for reasoning about possibility and necessity. On the one hand, the qua...
Knowledge Base Stratification and Merging Based on Degree of Support
"... Abstract. Most operators for merging multiple knowledge bases (where each is a set of formulae) aim to produce a knowledge base as output that best reflects the information available in the input. Whilst these operators have some valuable properties, they do not provide explicit information on the d ..."
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Cited by 3 (1 self)
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Abstract. Most operators for merging multiple knowledge bases (where each is a set of formulae) aim to produce a knowledge base as output that best reflects the information available in the input. Whilst these operators have some valuable properties, they do not provide explicit information on the degree to which each formula in the output has been, in some sense, supported by the different knowledge bases in the input. To address this, in this paper, we first define the degree of support that a formula receives from input knowledge bases. We then provide two ways of determining formulae which have the highest degree of support in the current collection of formulae in KBs, each of which gives a preference (or priority) over formulae that can be used to stratify the formulae in the output. We formulate these two preference criteria, and present an algorithm that given a set of knowledge bases as input, generates a stratified knowledge base as output. Following this, we define some merging operators based on the stratified base. Logical properties of these operators are investigated and a criterion for selecting merging operators is introduced. 1
Gestion De L'inconsistance Dans Les Bases De Connaissances : Une Approche Syntaxique Bas'ee Sur La Logique Des P'enalit'es
, 1994
"... : we consider a penalty logic, which is a formalization and an extension of (Pinkas 91 [18]). In this logic, we annotate each formula of a knowledge base with a price to pay when this formula is violated. A penalty logic knowledge base induces a nonmonotonic inference relation which belongs to the ..."
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Cited by 1 (1 self)
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: we consider a penalty logic, which is a formalization and an extension of (Pinkas 91 [18]). In this logic, we annotate each formula of a knowledge base with a price to pay when this formula is violated. A penalty logic knowledge base induces a nonmonotonic inference relation which belongs to the class of rational inference relations. We also consider a possible application of penalty logic for formalizing and solving discrete optimization problems. Motscl'es : bases de connaissances, traitement de l'inconsistance, inf'erence nonmonotone, sousth'eories pr'ef'er'ees, mod`eles pr'ef'erentiels, p'enalit'es, optimisation discr`ete. Keywords: knowledge bases, inconsistency handling, non monotonic reasoning, preferred subtheories, preferential models, penalties, discrete optimisation. 1 Introduction Les approches syntaxiques du raisonnement nonmonotone et de la r'evision des connaissances (voir par exemple (Nebel 91[17])) consistent `a consid'erer chaque formule d'une base de con...
Possibilistic Residuated Implication Logics with Applications
"... this paper, we will develop a class of logics for reasoning about qualitative and quantitative uncertainty. The semantics of the logics is uniformly based on possibility theory. Each logic in the class is parameterizedby a tnorm operation on [0,1], and we express the degree of implication between t ..."
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Cited by 1 (0 self)
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this paper, we will develop a class of logics for reasoning about qualitative and quantitative uncertainty. The semantics of the logics is uniformly based on possibility theory. Each logic in the class is parameterizedby a tnorm operation on [0,1], and we express the degree of implication between the possibilities of two formulas explicitly by using residuated implication with respect to the tnorm. The logics are then shown to be applicable to possibilistic reasoning, approximate reasoning, and nonmonotonic reasoning.
Gestion De L'inconsistance Dans Les Bases De Connaissances : Une Approche Syntaxique Bas'ee Sur La Logique Des P'enalit'es
, 1994
"... : we consider a penalty logic, which is a formalization and an extension of (Pinkas 91 [18]). In this logic, we annotate each formula of a knowledge base with a price to pay when this formula is violated. A penalty logic knowledge base induces a nonmonotonic inference relation which belongs to the ..."
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: we consider a penalty logic, which is a formalization and an extension of (Pinkas 91 [18]). In this logic, we annotate each formula of a knowledge base with a price to pay when this formula is violated. A penalty logic knowledge base induces a nonmonotonic inference relation which belongs to the class of rational inference relations. We also consider a possible application of penalty logic for formalizing and solving discrete optimization problems. Motscl'es : bases de connaissances, traitement de l'inconsistance, inf'erence nonmonotone, sousth'eories pr'ef'er'ees, mod`eles pr'ef'erentiels, p'enalit'es, optimisation discr`ete. Keywords: knowledge bases, inconsistency handling, non monotonic reasoning, preferred subtheories, preferential models, penalties, discrete optimisation. 1 Introduction Les approches syntaxiques du raisonnement nonmonotone et de la r'evision des connaissances (voir par exemple (Nebel 91[17])) consistent `a consid'erer chaque formule d'une base de con...