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We present the syntax and proof theory of a logic of argumentation, LA. We also outline the development of a category theoretic semantics for LA. LA is the core of a proof theoretic model for reasoning under uncertainty. In this logic, propositions are labelled with a representation of the arguments which support their validity. Arguments may then be aggregated to collect more information about the potential validity of the propositions of interest. We make the notion of aggregation primitive to the logic, and then define strength mappings from sets of arguments to one of a number of possible dictionaries. This provides a uniform framework which incorporates a number of numerical and symbolic techniques for assigning subjective confidences to propositions on the basis of their supporting arguments. These aggregation techniques are also described, with examples. Key words: Uncertain reasoning, epistemic probability, argumentation, non-classical logics, non-monotonic reasoning 1. Introd...

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.

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'...

: This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A so-called argumentative-consequence 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 paraconsistent-like 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...

this article I want to discuss some philosophical problems one encounters when trying to model the dynamics of epistemic states. Apart from being of interest in themselves, I believe that solutions to these problems will be crucial for any attempt to use computers to handle changes of knowledge systems. Problems concerning knowledge representation and the updating of such representations have become the focus of much recent research in artificial intelligence (AI)

This paper is meant to survey the literature pertaining to this debate, and to try to overcome misunderstandings and to supply access to many basic references that have addressed the "probability versus fuzzy set" challenge. This problem has not a single facet, as will be claimed here. Moreover it seems that a lot of controversies might have been avoided if protagonists had been patient enough to build a common language and to share their scientific backgrounds. The main points made here are as follows. i) Fuzzy set theory is a consistent body of mathematical tools. ii) Although fuzzy sets and probability measures are distinct, several bridges relating them have been proposed that should reconcile opposite points of view ; especially possibility theory stands at the cross-roads between fuzzy sets and probability theory. iii) Mathematical objects that behave like fuzzy sets exist in probability theory. It does not mean that fuzziness is reducible to randomness. Indeed iv) there are ways of approaching fuzzy sets and possibility theory that owe nothing to probability theory. Interpretations of probability theory are multiple especially frequentist versus subjectivist views (Fine [31]) ; several interpretations of fuzzy sets also exist. Some interpretations of fuzzy sets are in agreement with probability calculus and some are not. The paper is structured as follows : first we address some classical misunderstandings between fuzzy sets and probabilities. They must be solved before any discussion can take place. Then we consider probabilistic interpretations of membership functions, that may help in membership function assessment. We also point out nonprobabilistic interpretations of fuzzy sets. The next section examines the literature on possibility-probability transformati...

This paper investigates several methods for coping with inconsistency caused by multiple source information, by introducing suitable consequence relations capable of inferring non-trivial conclusions from an inconsistent stratified knowledge base. Some of these methods presuppose a revision step, namely a selection of one or several consistent subsets of formulas, and then classical inference is used for inferring from these subsets. Two alternative methods that do not require any revision step are studied: inference based on arguments, and a new approach called safely supported inference, where inconsistency is kept local. These two last methods look suitable when the inconsistency is due to the presence of several sources of information. The paper offers a comparative study of the various inference modes under inconsistency. 1 Introduction Inconsistency can be encountered in different reasoning tasks, in particular: - when reasoning with exception-tolerant generic knowledge, where ...

This paper is an investigation of the relationship between conditional objects obtained as a qualitative counterpart to conditional probabilities, and nonmonotonic reasoning. Roughly speaking, a conditional object can be seen as a generic rule which allows us to get a conclusion provided that the available information exactly corresponds to the "context" part of the conditional object. This gives freedom for possibly retracting previous conclusions when the available information becomes more specific. Viewed as an inference rule expressing a contextual belief, the conditional object is shown to possess all properties of a well-behaved nonmonotonic consequence relation when a suitable choice of connectives and deduction operation is made. Using previous results from Adams' conditional probabilistic logic, a logic of conditional objects is proposed. Its axioms and inference rules are those of preferential reasoning logic of Lehmann and colleagues. But the semantics relies on a three-valu...

This paper discusses belief revision under uncertain inputs in the framework of possibility theory. This framework is flexible enough to account for numerical and ordinal revision procedures. It is emphasized that revision under uncertain inputs can be understood in two different ways depending on whether the input is viewed as a constraint to be enforced, or as an unreliable piece of information. Two revision rules are proposed to implement these forms of revision. It is shown that M.A. Williams' transmutations, originally defined in the setting of Spohn's functions, can be captured in possibility theory, as well as Boutilier's natural revision. The use of conditioning greatly simplifies the description of these belief change operations. Lastly, preliminary results on implementing revision rules at the syntactic level are given. 1 - Introduction Belief revision in the sense of Alchourrón, Gärdenfors and Makinson (1985) (also called AGM revision) presupposes the existence of a so-call...