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76
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 194 (39 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
Argumentation in artificial intelligence
, 2007
"... Over the last ten years, argumentation has come to be increasingly central as a core study within Artificial Intelligence (AI). The articles forming this volume reflect a variety of important trends, developments, and applications covering a range of current topics relating to the theory and applica ..."
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Cited by 90 (6 self)
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Over the last ten years, argumentation has come to be increasingly central as a core study within Artificial Intelligence (AI). The articles forming this volume reflect a variety of important trends, developments, and applications covering a range of current topics relating to the theory and applications of argumentation. Our aims in this introduction are, firstly, to place these contributions in the context of the historical foundations of argumentation in AI and, subsequently, to discuss a number of themes that have emerged in recent years resulting in a significant broadening of the areas in which argumentation based methods are used. We begin by presenting a brief overview of the issues of interest within the classical study of argumentation: in particular, its relationship— in terms of both similarities and important differences—to traditional concepts of logical reasoning and mathematical proof. We continue by outlining how a number of foundational contributions provided the basis for the formulation of argumentation models and their promotion in AI related settings and then consider a number of new themes that have emerged in recent years, many of which provide the principal topics of the research presented in this volume.
Possibility theory and statistical reasoning
 Computational Statistics & Data Analysis Vol
, 2006
"... Numerical possibility distributions can encode special convex families of probability measures. The connection between possibility theory and probability theory is potentially fruitful in the scope of statistical reasoning when uncertainty due to variability of observations should be distinguished f ..."
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Cited by 59 (4 self)
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Numerical possibility distributions can encode special convex families of probability measures. The connection between possibility theory and probability theory is potentially fruitful in the scope of statistical reasoning when uncertainty due to variability of observations should be distinguished from uncertainty due to incomplete information. This paper proposes an overview of numerical possibility theory. Its aim is to show that some notions in statistics are naturally interpreted in the language of this theory. First, probabilistic inequalites (like Chebychev’s) offer a natural setting for devising possibility distributions from poor probabilistic information. Moreover, likelihood functions obey the laws of possibility theory when no prior probability is available. Possibility distributions also generalize the notion of confidence or prediction intervals, shedding some light on the role of the mode of asymmetric probability densities in the derivation of maximally informative interval substitutes of probabilistic information. Finally, the simulation of fuzzy sets comes down to selecting a probabilistic representation of a possibility distribution, which coincides with the Shapley value of the corresponding consonant capacity. This selection process is in agreement with Laplace indifference principle and is closely connected with the mean interval of a fuzzy interval. It sheds light on the “defuzzification ” process in fuzzy set theory and provides a natural definition of a subjective possibility distribution that sticks to the Bayesian framework of exchangeable bets. Potential applications to risk assessment are pointed out. 1
Probabilistic Default Reasoning with Conditional Constraints
 ANN. MATH. ARTIF. INTELL
, 2000
"... We present an approach to reasoning from statistical and subjective knowledge, which is based on a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. More precisely, we introduce the notions of , lexicographic, ..."
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Cited by 38 (18 self)
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We present an approach to reasoning from statistical and subjective knowledge, which is based on a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. More precisely, we introduce the notions of , lexicographic, and conditional entailment for conditional constraints, which are probabilistic generalizations of Pearl's entailment in system , Lehmann's lexicographic entailment, and Geffner's conditional entailment, respectively. We show that the new formalisms have nice properties. In particular, they show a similar behavior as referenceclass reasoning in a number of uncontroversial examples. The new formalisms, however, also avoid many drawbacks of referenceclass reasoning. More precisely, they can handle complex scenarios and even purely probabilistic subjective knowledge as input. Moreover, conclusions are drawn in a global way from all the available knowledge as a whole. We then show that the new formalisms also have nice general nonmonotonic properties. In detail, the new notions of , lexicographic, and conditional entailment have similar properties as their classical counterparts. In particular, they all satisfy the rationality postulates proposed by Kraus, Lehmann, and Magidor, and they have some general irrelevance and direct inference properties. Moreover, the new notions of  and lexicographic entailment satisfy the property of rational monotonicity. Furthermore, the new notions of , lexicographic, and conditional entailment are proper generalizations of both their classical counterparts and the classical notion of logical entailment for conditional constraints. Finally, we provide algorithms for reasoning under the new formalisms, and we analyze its computational com...
H.: Towards a possibilistic logic handling of preferences
 Applied Intelligence
, 2001
"... The classical way of encoding preferences in decision theory is by means of utility or value functions. However agents are not always able to deliver such a function directly. In this paper, we relate three different ways of specifying preferences, namely by means of a set of particular types of con ..."
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Cited by 28 (9 self)
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The classical way of encoding preferences in decision theory is by means of utility or value functions. However agents are not always able to deliver such a function directly. In this paper, we relate three different ways of specifying preferences, namely by means of a set of particular types of constraints on the utility function, by means of an ordered set of priorit ized goals expressed by logical propositions, and by means of an ordered set of subsets of possible candidates reaching the same level of satisfaction. These different expression modes can be handled in a weighted logical setting, here the one of possibilistic logic. The aggregation of preferences pertaining to different criteria can then be handled by fusing sets of prioritized goals. Apart from a better expressivity, the benefits of a logical representation of preferences are to put them in a suitable format for reasoning purposes, or for modifying or revising them. 1.
Logical Representation and Computation of Optimal Decisions in a Qualitative Setting
 In Proceedings of the Fifteenth National Conference on Artificial Intelligence
, 1998
"... This paper describes a logical machinery for computing decisions based on an ATMS procedure, where the available knowledge on the state of the world is described by a possibilistic propositional logic base (i.e., a collection of logical statements associated with qualitative certainty levels). ..."
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Cited by 23 (8 self)
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This paper describes a logical machinery for computing decisions based on an ATMS procedure, where the available knowledge on the state of the world is described by a possibilistic propositional logic base (i.e., a collection of logical statements associated with qualitative certainty levels). The preferences of the user are also described by another possibilistic logic base whose formula weights are interpreted in terms of priorities and formulas express goals. Two attitudes are allowed for the decision maker: a pessimistic uncertaintyaverse one and an optimistic one. The computed decisions are in agreement with a qualitative counterpart to classical expected utility theory for decision under uncertainty.
Probabilistic Logic under Coherence: Complexity and Algorithms
 In Proceedings ISIPTA01
, 2001
"... We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore the relationship between coherencebased and classical modeltheoretic probabilistic logic. Interestingly, we show that the notions of gcoherence and of gcoherent entailment can be expre ..."
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Cited by 23 (11 self)
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We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore the relationship between coherencebased and classical modeltheoretic probabilistic logic. Interestingly, we show that the notions of gcoherence and of gcoherent entailment can be expressed by combining notions in modeltheoretic probabilistic logic with concepts from default reasoning. Using these results, we analyze the computational complexity of probabilistic reasoning under coherence. Moreover, we present new algorithms for deciding gcoherence and for computing tight gcoherent intervals, which reduce these tasks to standard reasoning tasks in modeltheoretic probabilistic logic. Thus, efficient techniques for modeltheoretic probabilistic reasoning can immediately be applied for probabilistic reasoning under coherence, for example, column generation techniques. We then describe two other interesting techniques for efficient modeltheoretic probabilistic reasoning in the conjunctive case.
Weak nonmonotonic probabilistic logics
, 2004
"... Towards probabilistic formalisms for resolving local inconsistencies under modeltheoretic probabilistic entailment, we present probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment. We then analyze the nonmonotonic and semantic properties of the new ..."
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Cited by 23 (6 self)
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Towards probabilistic formalisms for resolving local inconsistencies under modeltheoretic probabilistic entailment, we present probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment. We then analyze the nonmonotonic and semantic properties of the new notions of entailment. In particular, we show that they satisfy the rationality postulates of System P and the property of Rational Monotonicity. Moreover, we show that modeltheoretic probabilistic entailment is stronger than the new notion of lexicographic entailment, which in turn is stronger than the new notion of entailment in System Z. As an important feature of the new notions of entailment in System Z and lexicographic entailment, we show that they coincide with modeltheoretic probabilistic entailment whenever there are no local inconsistencies. We also show that the new notions of entailment in System Z and lexicographic entailment are proper generalizations of their classical counterparts. Finally, we present algorithms for reasoning under the new formalisms, and we give a precise picture of its computational complexity.
Probabilistic Logic under Coherence, ModelTheoretic Probabilistic Logic, and Default Reasoning
 Journal of Applied NonClassical Logics
"... We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore the relationship between coherencebased and modeltheoretic probabilistic logic. Interestingly, we show that the notions of gcoherence and of gcoherent entailment can be expressed by co ..."
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Cited by 23 (7 self)
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We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore the relationship between coherencebased and modeltheoretic probabilistic logic. Interestingly, we show that the notions of gcoherence and of gcoherent entailment can be expressed by combining notions in modeltheoretic probabilistic logic with concepts from default reasoning. Crucially, we even show that probabilistic reasoning under coherence is a probabilistic generalization of default reasoning in system P. That is, we provide a new probabilistic semantics for system P, which is neither based on infinitesimal probabilities nor on atomicbound (or also bigstepped) probabilities. These results also give new insight into default reasoning with conditional objects.
Default Reasoning from Conditional Knowledge Bases: Complexity and Tractable Cases
 Artif. Intell
, 2000
"... Conditional knowledge bases have been proposed as belief bases that include defeasible rules (also called defaults) of the form " ! ", which informally read as "generally, if then ." Such rules may have exceptions, which can be handled in different ways. A number of entailment ..."
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Cited by 19 (11 self)
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Conditional knowledge bases have been proposed as belief bases that include defeasible rules (also called defaults) of the form " ! ", which informally read as "generally, if then ." Such rules may have exceptions, which can be handled in different ways. A number of entailment semantics for conditional knowledge bases have been proposed in the literature. However, while the semantic properties and interrelationships of these formalisms are quite well understood, about their computational properties only partial results are known so far. In this paper, we fill these gaps and first draw a precise picture of the complexity of default reasoning from conditional knowledge bases: Given a conditional knowledge base KB and a default ! , does KB entail ! ? We classify the complexity of this problem for a number of wellknown approaches (including Goldszmidt et al.'s maximum entropy approach and Geffner's conditional entailment), where we consider the general propositional case as well as natural syntactic restrictions (in particular, to Horn and literalHorn conditional knowledge bases). As we show, the more sophisticated semantics for conditional knowledge bases are plagued with intractability in all these fragments. We thus explore cases in which these semantics are tractable, and find that most of them enjoy this property on feedbackfree Horn conditional knowledge bases, which constitute a new, meaningful class of conditional knowledge bases. Furthermore, we generalize previous tractability results from Horn to qHorn conditional knowledge bases, which allow for a limited use of disjunction. Our results complement and extend previous results, and contribute in refining the tractability/intractability frontier of default reasoning from conditional know...