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215
Nonmonotonic Reasoning, Preferential Models and Cumulative Logics
, 1990
"... Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not enjoy, i.e. monotonicity. We study here general patterns of ..."
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Cited by 544 (13 self)
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Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not enjoy, i.e. monotonicity. We study here general patterns of nonmonotonic reasoning and try to isolate properties that could help us map the field of nonmonotonic reasoning by reference to positive properties. We concentrate on a number of families of nonmonotonic consequence relations, defined in the style of Gentzen [13]. Both prooftheoretic and semantic points of view are developed in parallel. The former point of view was pioneered by D. Gabbay in [10], while the latter has been advocated by Y. Shoham in [38]. Five such families are defined and characterized by representation theorems, relating the two points of view. One of the families of interest, that of preferential relations, turns out to have been studied by E. Adams in [2]. The pr...
What Does a Conditional Knowledge Base Entail?
 Artificial Intelligence
, 1989
"... This paper presents a logical approach to nonmonotonic reasoning based on the notion of a nonmonotonic consequence relation. A conditional knowledge base, consisting of a set of conditional assertions of the type if . . . then . . . , represents the explicit defeasible knowledge an agent has abo ..."
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Cited by 236 (6 self)
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This paper presents a logical approach to nonmonotonic reasoning based on the notion of a nonmonotonic consequence relation. A conditional knowledge base, consisting of a set of conditional assertions of the type if . . . then . . . , represents the explicit defeasible knowledge an agent has about the way the world generally behaves. We look for a plausible definition of the set of all conditional assertions entailed by a conditional knowledge base. In a previous paper [17], S. Kraus and the authors defined and studied preferential consequence relations. They noticed that not all preferential relations could be considered as reasonable inference procedures. This paper studies a more restricted class of consequence relations, rational relations. It is argued that any reasonable nonmonotonic inference procedure should define a rational relation. It is shown that the rational relations are exactly those that may be represented by a ranked preferential model, or by a (nonstandard) probabilistic model.
System Z: a natural ordering of defaults with tractable applications to default reasoning
, 1990
"... Recent progress towards unifying the probabilistic and preferential models semantics for nonmonotonic reasoning has led to a remarkable observation: Any consistent system of default rules imposes an unambiguous and natural ordering on these rules which, to emphasize its simple and basic character, ..."
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Cited by 167 (0 self)
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Recent progress towards unifying the probabilistic and preferential models semantics for nonmonotonic reasoning has led to a remarkable observation: Any consistent system of default rules imposes an unambiguous and natural ordering on these rules which, to emphasize its simple and basic character, we term &quot;Zordering. &quot; This ordering can be used with various levels of refinement, to prioritize conflicting arguments, to rank the degree of abnormality of states of the world, and to define plausible consequence relationships. This paper defines the Zordering, briefly mentions its semantical origins, and iUustrates two simple entailment relationships induced by the ordering. Two extensions are then described, maximumentropy and conditional entailment, which trade in computational simplicity for semantic refinements. 1. Description We begin with a set of rules R = {r: %. ~ 6,} where % and [~r are propositional formulas over a finite alphabet of literals, ando denotes a new connective to be given default interpretations later on. A truth valuation of the fiterals in the language will be called a model. A model M is said to verify a rule ot ~ ifM ~ot ^ [3(i.e., o~and ~ are both true in M), and to falsify ot ~ ~ifM ~A ~ 13. Given a set R of such rules, we first define the relation of toleration.
Logical Models of Argument
 ACM COMPUTING SURVEYS
, 2000
"... Logical models of argument formalize commonsense reasoning while taking process and computation seriously. This survey discusses the main ideas which characterize different logical models of argument. It presents the formal features of a few main approaches to the modeling of argumentation. We trace ..."
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Cited by 140 (32 self)
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Logical models of argument formalize commonsense reasoning while taking process and computation seriously. This survey discusses the main ideas which characterize different logical models of argument. It presents the formal features of a few main approaches to the modeling of argumentation. We trace the
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 99 (38 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.
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 79 (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]:
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 70 (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...
Modeling Agents as Qualitative Decision Makers
 Artificial Intelligence
, 1997
"... We investigate the semantic foundations of a method for modeling agents as entities with a mental state which was suggested by McCarthy and by Newell. Our goals are to formalize this modeling approach and its semantics, to understand the theoretical and practical issues that it raises, and to addres ..."
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Cited by 48 (0 self)
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We investigate the semantic foundations of a method for modeling agents as entities with a mental state which was suggested by McCarthy and by Newell. Our goals are to formalize this modeling approach and its semantics, to understand the theoretical and practical issues that it raises, and to address some of them. In particular, this requires specifying the model's parameters and how these parameters are to be assigned (i.e., their grounding). We propose a basic model in which the agent is viewed as a qualitative decision maker with beliefs, preferences, and decision strategy; and we show how these components would determine the agent's behavior. We ground this model in the agent's interaction with the world, namely, in its actions. This is done by viewing model construction as a constraint satisfaction problem in which we search for a model consistent with the agent's behavior and with our general background knowledge. In addition, we investigate the conditions under which a mental st...
Probabilistic Deduction with Conditional Constraints over Basic Events
 J. Artif. Intell. Res
, 1999
"... We study the problem of probabilistic deduction with conditional constraints over basic events. We show that globally complete probabilistic deduction with conditional constraints over basic events is NPhard. We then concentrate on the special case of probabilistic deduction in conditional constrai ..."
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Cited by 46 (30 self)
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We study the problem of probabilistic deduction with conditional constraints over basic events. We show that globally complete probabilistic deduction with conditional constraints over basic events is NPhard. We then concentrate on the special case of probabilistic deduction in conditional constraint trees. We elaborate very efficient techniques for globally complete probabilistic deduction. In detail, for conditional constraint trees with point probabilities, we present a local approach to globally complete probabilistic deduction, which runs in linear time in the size of the conditional constraint trees. For conditional constraint trees with interval probabilities, we show that globally complete probabilistic deduction can be done in a global approach by solving nonlinear programs. We show how these nonlinear programs can be transformed into equivalent linear programs, which are solvable in polynomial time in the size of the conditional constraint trees. 1. Introduction Dealing wit...
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 45 (8 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...