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397
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...
The Value of the Four Values
 Artificial Intelligence
, 1998
"... In his wellknown paper "How computer should think" ([Be77b]) Belnap argues that four valued semantics is a very suitable setting for computerized reasoning. In this paper we vindicate this thesis by showing that the logical role that the fourvalued structure has among Ginsberg's wellknown bilatti ..."
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Cited by 62 (6 self)
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In his wellknown paper "How computer should think" ([Be77b]) Belnap argues that four valued semantics is a very suitable setting for computerized reasoning. In this paper we vindicate this thesis by showing that the logical role that the fourvalued structure has among Ginsberg's wellknown bilattices is similar to the role that the twovalued algebra has among Boolean algebras. Specifically, we provide several theorems that show that the most useful bilatticevalued logics can actually be characterized as fourvalued inference relations. In addition, we compare the use of threevalued logics with the use of fourvalued logics, and show that at least for the task of handling inconsistent or uncertain information, the comparison is in favor of the latter. Keyworkds: Bilattices, Paraconsistency, Multiplevalued systems, Preferential logics, Reasoning. 1 Introduction In [Be77a, Be77b] Belnap introduced a logic intended to deal in a useful way with inconsistent and incomplete information....
Managing Uncertainty and Vagueness in Description Logics for the Semantic Web
, 2007
"... Ontologies play a crucial role in the development of the Semantic Web as a means for defining shared terms in web resources. They are formulated in web ontology languages, which are based on expressive description logics. Significant research efforts in the semantic web community are recently direct ..."
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Cited by 58 (7 self)
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Ontologies play a crucial role in the development of the Semantic Web as a means for defining shared terms in web resources. They are formulated in web ontology languages, which are based on expressive description logics. Significant research efforts in the semantic web community are recently directed towards representing and reasoning with uncertainty and vagueness in ontologies for the Semantic Web. In this paper, we give an overview of approaches in this context to managing probabilistic uncertainty, possibilistic uncertainty, and vagueness in expressive description logics for the Semantic Web.
A Classification Theory of Semantics of Normal Logic Programs: II. Weak Properties
 FUNDAMENTA INFORMATICAE
, 1995
"... Our aim in this article is to supplement the set of strong properties introduced in the preceding article ([Dix94]) with a set of weak principles in order to characterize semantics of logic programs. In [Dix94] we introduced our point of view: we observed that all semantics induce in a natural way a ..."
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Cited by 56 (0 self)
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Our aim in this article is to supplement the set of strong properties introduced in the preceding article ([Dix94]) with a set of weak principles in order to characterize semantics of logic programs. In [Dix94] we introduced our point of view: we observed that all semantics induce in a natural way a sceptical nonmonotonic entailment relation SEM scept . We ask for the properties of these sceptical relations and use them to describe all possible semantics. We collect in this paper serious shortcomings of some semantics proposed recently. Their strange behaviour led us to formulate in a natural way certain principles to avoid these problems. We argue that any wellbehaved semantics should satisfy these principles. The main results state that our list of weak principles is complete in the following sense: any wellbehavedsemantics is an extension of the wellfounded semantics WFS and coincides for stratified programs with Apt, Blair, and Walker's supported model M supp P . We also...
Logic and Databases: a 20 Year Retrospective
, 1996
"... . At a workshop held in Toulouse, France in 1977, Gallaire, Minker and Nicolas stated that logic and databases was a field in its own right (see [131]). This was the first time that this designation was made. The impetus for this started approximately twenty years ago in 1976 when I visited Gallaire ..."
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Cited by 55 (1 self)
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. At a workshop held in Toulouse, France in 1977, Gallaire, Minker and Nicolas stated that logic and databases was a field in its own right (see [131]). This was the first time that this designation was made. The impetus for this started approximately twenty years ago in 1976 when I visited Gallaire and Nicolas in Toulouse, France, which culminated in a workshop held in Toulouse, France in 1977. It is appropriate, then to provide an assessment as to what has been achieved in the twenty years since the field started as a distinct discipline. In this retrospective I shall review developments that have taken place in the field, assess the contributions that have been made, consider the status of implementations of deductive databases and discuss the future of work in this area. 1 Introduction As described in [234], the use of logic and deduction in databases started in the late 1960s. Prominent among the developments was the work by Levien and Maron [202, 203, 199, 200, 201] and Kuhns [1...
Possibilistic logic, preferential models, nonmonotonicity and related issues
 In Proc. Twelfth International Joint Conference on Artificial Intelligence (IJCAI '91
, 1991
"... The links between Shoham's preference logic and possibilistic logic, a numerical logic of uncertainty based on Zadeh's possibility measures, are investigated. Starting from a fuzzy set of preferential interpretations of a propositional theory, we prove that the notion of preferential entailment is c ..."
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Cited by 51 (8 self)
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The links between Shoham's preference logic and possibilistic logic, a numerical logic of uncertainty based on Zadeh's possibility measures, are investigated. Starting from a fuzzy set of preferential interpretations of a propositional theory, we prove that the notion of preferential entailment is closely related to a previously introduced notion of conditional possibility. Conditional possibility is then shown to possess all properties (originally stated by Gabbay) of a wellbehaved nonmonotonic consequence relation. We obtain the possibilistic counterpart of Adams ' esemantics of conditional probabilities which is the basis of the probabilistic model of nonmonotonic logic proposed by Geffner and Pearl. Lastly we prove that our notion of possibilistic entailment is the one at work in possibilistic logic, a logic that handles uncertain propositional formulas, where uncertainty is modelled by degrees of necessity, and where partial inconsistency is allowed. Considering the formerly established close links between Gardenfors'epistemic entrenchment and necessity measures, what this paper proposes is a new way of relating belief revision and nonmonotonic inference, namely via possibility theory. 1
Investigating Aboutness Axioms using Information Fields
 In Proceedings of ACM SIGIR Conference on Research and Development in Information Retrieval
, 1994
"... This article proposes a framework, a so called information field, which allows information retrieval mechanisms to be compared inductively instead of experimentally. Such a comparison occurs as follows: Both retrieval mechanisms are first mapped to an associated information field. Within the field, ..."
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Cited by 44 (22 self)
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This article proposes a framework, a so called information field, which allows information retrieval mechanisms to be compared inductively instead of experimentally. Such a comparison occurs as follows: Both retrieval mechanisms are first mapped to an associated information field. Within the field, the axioms that drive the retrieval process can be filtered out. In this way, the implicit assumptions governing an information retrieval mechanism can be brought to light. The retrieval mechanisms can then be compared according to which axioms they are governed by. Using this method it is shown that Boolean retrieval is more powerful than a strict form of coordinate retrieval. The salient point is not this result in itself, but how the result was achieved. 1 Introduction The logic based approach to information retrieval has been around for some time now. So far, a number of inference mechanisms, both strict and plausible, have been proposed for driving the retrieval process [15, 6, 4, 12]....
ContraryToDuty Reasoning with Preferencebased Dyadic Obligations
, 1999
"... this paper we introduce Prohairetic Deontic Logic (PDL), a preferencebased ..."
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Cited by 44 (19 self)
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this paper we introduce Prohairetic Deontic Logic (PDL), a preferencebased
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.