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190
Toward a Logic for Qualitative Decision Theory
 In Proceedings of the KR'94
, 1992
"... We present a logic for representing and reasoning with qualitative statements of preference and normality and describe how these may interact in decision making under uncertainty. Our aim is to develop a logical calculus that employs the basic elements of classical decision theory, namely proba ..."
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Cited by 217 (3 self)
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We present a logic for representing and reasoning with qualitative statements of preference and normality and describe how these may interact in decision making under uncertainty. Our aim is to develop a logical calculus that employs the basic elements of classical decision theory, namely probabilities, utilities and actions, but exploits qualitative information about these elements directly for the derivation of goals. Preferences and judgements of normality are captured in a modal/conditional logic, and a simple model of action is incorporated. Without quantitative information, decision criteria other than maximum expected utility are pursued. We describe how techniques for conditional default reasoning can be used to complete information about both preferences and normality judgements, and we show how maximin and maximax strategies can be expressed in our logic.
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 105 (42 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.
Reasoning about priorities in default logic, in
 Proceedings of the 12th National Conference on Artificial Intelligence (MIT
, 1994
"... In this paper we argue that for realistic applications involving default reasoning it is necessary to reason about the priorities of defaults. Existing approaches require the knowledge engineer to explicitly state all relevant priorities which are then handled in an extralogical manner, or they are ..."
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Cited by 102 (7 self)
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In this paper we argue that for realistic applications involving default reasoning it is necessary to reason about the priorities of defaults. Existing approaches require the knowledge engineer to explicitly state all relevant priorities which are then handled in an extralogical manner, or they are restricted to priorities based on specificity, neglecting other relevant criteria. We present an approach where priority information can be represented within the logical language. Our approach is based on PDL, a prioritized extension of Reiter’s Default Logic recently proposed by the same author. In PDL the generation of extensions is controlled by an ordering of the defaults. This property is used here in the following way: we first build Reiter extensions of a given default theory. These extensions contain explicit information about the priorities of defaults. We then eliminate every extension E that cannot be reconstructed as a PDL extension based on a default ordering that is compatible with the priority information in E. An example from legal reasoning illustrates the power of our approach. 1.
Logical preference representation and combinatorial vote,
 Annals of Mathematics and Artificial Intelligence
, 2004
"... We introduce the notion of combinatorial vote, where a group of agents (or voters) is supposed to express preferences and come to a common decision concerning a set of nonindependent variables to assign. We study two key issues pertaining to combinatorial vote, namely preference representation and ..."
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Cited by 96 (16 self)
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We introduce the notion of combinatorial vote, where a group of agents (or voters) is supposed to express preferences and come to a common decision concerning a set of nonindependent variables to assign. We study two key issues pertaining to combinatorial vote, namely preference representation and the automated choice of an optimal decision. For each of these issues, we briefly review the state of the art, we try to define the main problems to be solved and identify their computational complexity.
Argumentative Inference in Uncertain and Inconsistent Knowledge Bases
 In Proceedings of Uncertainty in Artificial Intelligence
, 1993
"... : This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A socalled argumentativeconsequence relation, taking into account the existence of consistent arguments in favor of a conclusion and the absence of consistent arguments in favor of its contrary, is ..."
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Cited by 90 (3 self)
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: This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A socalled argumentativeconsequence relation, taking into account the existence of consistent arguments in favor of a conclusion and the absence of consistent arguments in favor of its contrary, is particularly investigated. Flat knowledge bases, i.e. without any priority between their elements, as well as prioritized ones where some elements are considered as more strongly entrenched than others are studied under the different consequence relations which are considered. Lastly a paraconsistentlike treatment of prioritized knowledge bases is proposed, where both the level of entrenchment and the level of paraconsistency attached to a formula are propagated. The priority levels are handled in the framework of possibility theory. Keywords: Inconsistency; consequence relation; prioritized knowledge base; uncertainty; possibilistic logic; possibility theory. Submitted to the Ninth Annual...
Plausibility Measures and Default Reasoning
 Journal of the ACM
, 1996
"... this paper: default reasoning. In recent years, a number of different semantics for defaults have been proposed, such as preferential structures, fflsemantics, possibilistic structures, and rankings, that have been shown to be characterized by the same set of axioms, known as the KLM properties. W ..."
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Cited by 87 (12 self)
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this paper: default reasoning. In recent years, a number of different semantics for defaults have been proposed, such as preferential structures, fflsemantics, possibilistic structures, and rankings, that have been shown to be characterized by the same set of axioms, known as the KLM properties. While this was viewed as a surprise, we show here that it is almost inevitable. In the framework of plausibility measures, we can give a necessary condition for the KLM axioms to be sound, and an additional condition necessary and sufficient to ensure that the KLM axioms are complete. This additional condition is so weak that it is almost always met whenever the axioms are sound. In particular, it is easily seen to hold for all the proposals made in the literature. Categories and Subject Descriptors: F.4.1 [Mathematical Logic and Formal Languages]:
Revision Sequences and Nested Conditionals
"... The truth conditions for conditional sentences have been wellstudied, but few compelling attempts have been made to define means of evaluating iterated or nested conditionals. In particular, most approaches impose very few constraints on the set of conditionals an agent can hold after revision of i ..."
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Cited by 83 (4 self)
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The truth conditions for conditional sentences have been wellstudied, but few compelling attempts have been made to define means of evaluating iterated or nested conditionals. In particular, most approaches impose very few constraints on the set of conditionals an agent can hold after revision of its belief set. In this paper we describe the method of natural revision that ensures the preservation of conditional beliefs after revision by an objective belief. Our model, based on a simple modal logic for beliefs and conditionals, extends the AGM theory of belief revision to account for sentiences of objective revisions of a belief set. This model of revision ensures that an agent makes as few changes as possible to the conditional component of its belief set. Adopting the Ramsey test, natural revision provides truth conditions for arbitrary rightnested conditionals. We show that the problem of determining acceptance of any such nested conditional can be reduced to acceptance tests for unnested conditionals, indicating that iterated revision can be simulated by virtual updates. We also briefly describe certain reductions to (sometimes tractable) propositional inference, and other informational properties.
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 closu ..."
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Cited by 78 (22 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...
Iterated Revision and Minimal Change of Conditional Beliefs
 JOURNAL OF PHILOSOPHICAL LOGIC
, 1995
"... We describe a model of iterated belief revision that extends the AGM theory of revision to account for the effect of a revision on the conditional beliefs of an agent. In particular, this model ensures that an agent makes as few changes as possible to the conditional component of its belief set. Ado ..."
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Cited by 51 (0 self)
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We describe a model of iterated belief revision that extends the AGM theory of revision to account for the effect of a revision on the conditional beliefs of an agent. In particular, this model ensures that an agent makes as few changes as possible to the conditional component of its belief set. Adopting the Ramsey test, minimal conditional revision provides acceptance conditions for arbitrary rightnested conditionals. We show that problem of determining acceptance of any such nested conditional can be reduced to acceptance tests for unnested conditionals. Thus, iterated revision can be accomplished in a “virtual” manner, using uniterated revision.
Statistical Foundations for Default Reasoning
, 1993
"... We describe a new approach to default reasoning, based on a principle of indifference among possible worlds. We interpret default rules as extreme statistical statements, thus obtaining a knowledge base KB comprised of statistical and firstorder statements. We then assign equal probability to all w ..."
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Cited by 49 (7 self)
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We describe a new approach to default reasoning, based on a principle of indifference among possible worlds. We interpret default rules as extreme statistical statements, thus obtaining a knowledge base KB comprised of statistical and firstorder statements. We then assign equal probability to all worlds consistent with KB in order to assign a degree of belief to a statement '. The degree of belief can be used to decide whether to defeasibly conclude '. Various natural patterns of reasoning, such as a preference for more specific defaults, indifference to irrelevant information, and the ability to combine independent pieces of evidence, turn out to follow naturally from this technique. Furthermore, our approach is not restricted to default reasoning; it supports a spectrum of reasoning, from quantitative to qualitative. It is also related to other systems for default reasoning. In particular, we show that the work of [ Goldszmidt et al., 1990 ] , which applies maximum entropy ideas t...