We survey here various approaches which were proposed to incorporate negation in logic programs. We concentrate on the proof-theoretic and model-theoretic issues and the relationships between them.

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The idea of ordering plays a basic role in commonsense reasoning for addressing three interrelated tasks: inconsistency handling, belief revision and plausible inference. We study the behavior of non-monotonic inferences induced by various methods for priority-based handling of inconsistent sets of classical formulas. One of them is based on a lexicographic ordering of maximal consistent subsets, and refines Brewka's preferred sub-theories. This new approach leads to a non-monotonic inference which satisfies the "rationality " property while solving the problem of blocking of property inheritance. It differs from and improves previous equivalent approaches such as Gardenfors and Makinson's expectation-based inference, Pearl's System Z and possibilistic logic. 1

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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

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 rank-order default rules. In this paper we show how to encode such a rank-ordered 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.

The lexicographic closure of any given finite set D of normal defaults is defined. A conditional assertion a b is in this lexicographic closure if, given the defaults D and the fact a, one would conclude b. The lexicographic closure is essentially a rational extension of D, and of its rational closure, defined in a previous paper. It provides a logic of normal defaults that is different from the one proposed by R. Reiter and that is rich enough not to require the consideration of non-normal defaults. A large number of examples are provided to show that the lexicographic closure corresponds to the basic intuitions behind Reiter's logic of defaults. 1 Plan of this paper Section 2 is a general introduction, describing the goal of this paper, in relation with Reiter's Default Logic and the program proposed in [12] by Lehmann and Magidor. Section 3 first discusses at length some general principles of the logic of defaults, with many examples, and, then, puts this paper in perspe...

this paper: default reasoning. In recent years, a number of different semantics for defaults have been proposed, such as preferential structures, ffl-semantics, 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]:

Abstract. 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 non-independent 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.

This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A so-called argued consequence relation, taking into account the existence of consistent arguments in favour of a conclusion and the absence of consistent arguments in favour of its contrary, is particularly investigated. Flat knowledge bases, i.e., without any priority between their elements, are studied under different inconsistency-tolerant consequence relations, namely the so-called argumentative, free, universal, existential, cardinality-based, and paraconsistent consequence relations. The syntax-sensitivity of these consequence relations is studied. A companion paper is devoted to the case where priorities exist between the pieces of information in the knowledge base. Key words: inconsistency, argumentation, nonmonotonic reasoning, syntaxsensitivity. * Some of the results contained in this paper were presented at the Ninth Conference on Uncertainty in Artificial Intelligence (UAI'...