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11Modern Versus Classical Structures of Opposition: A DiscussionLogica Universalis 1-28. forthcoming.The aim of this work is to revisit the proposal made by Dag Westerståhl a decade ago when he provided a modern reading of the traditional square of opposition and of related structures. We propose a formalization of this modern view and contrast it with the classical one. We discuss what may be a modern hexagon of opposition and a modern cube, and show their interest in particular for relating quantitative expressions.
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6An elementary belief function logicJournal of Applied Non-Classical Logics 33 (3-4): 582-605. 2023.1. There are two distinct lines of research that aim at modelling belief and knowledge: modal logic and uncertainty theories. Modal logic extends classical logic by introducing knowledge or belief...
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Possibility theory, probability theory, and muliple-valued logics: A clarificationAnnals of Mathematics and Artificial Intelligence 32 35--66. 2001.
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43Aggregation of decomposable measures with application to utility theoryTheory and Decision 41 (1): 59-95. 1996.
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55A modal theorem-preserving translation of a class of three-valued logics of incomplete informationJournal of Applied Non-Classical Logics 23 (4): 321-352. 2013.There are several three-valued logical systems that form a scattered landscape, even if all reasonable connectives in three-valued logics can be derived from a few of them. Most papers on this subject neglect the issue of the relevance of such logics in relation with the intended meaning of the third truth-value. Here, we focus on the case where the third truth-value means unknown, as suggested by Kleene. Under such an understanding, we show that any truth-qualified formula in a large range of t…Read more
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7Encoding classical fusion in ordered knowledge bases frameworkLinköping Electronic Articles in Computer and Information Science 5. 2000.The problem of merging multiple sources information is central in many information processing areas such as databases integrating problems, multiple criteria decision making, expert opinion pooling, etc. Recently, several approaches have been proposed to merge classical propositional bases, or sets of (non-prioritized) goals. These approaches are in general semantically defined. Like in belief revision, they use priorities, generally based on Dalal's distance, for merging the classical bases and…Read more
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5Corrigendum to “Qualitative decision theory with preference relations and comparative uncertainty: an axiomatic approach” [Artificial Intelligence 148 (1–2) (2003) 219–260] (review)Artificial Intelligence 171 (5-6): 361-362. 2007.
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12Fuzzy set and possibility theory-based methods in artificial intelligenceArtificial Intelligence 148 (1-2): 1-9. 2003.
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7Qualitative decision theory with preference relations and comparative uncertainty: An axiomatic approachArtificial Intelligence 148 (1-2): 219-260. 2003.
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4Special Issue of the journal Artificial Intelligence on “Fuzzy Set and Possibility Theory-Based Methods in Artificial Intelligence”Artificial Intelligence 127 (2): 269-270. 2001.
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5Generalized possibilistic logic: Foundations and applications to qualitative reasoning about uncertaintyArtificial Intelligence 252 (C): 139-174. 2017.
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8Nonmonotonic reasoning, conditional objects and possibility theoryArtificial Intelligence 92 (1-2): 259-276. 1997.
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2Special Issue of the journal Artificial Intelligence on “Fuzzy Set and Possibility Theory-Based Methods in Artificial Intelligence”Artificial Intelligence 128 (1-2): 245-246. 2001.
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10Special Issue of the journal Artificial Intelligence on “Fuzzy Set and Possibility Theory-Based Methods in Artificial Intelligence”Artificial Intelligence 127 (1): 163-164. 2001.
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19Structures of Opposition and Comparisons: Boolean and Gradual CasesLogica Universalis 14 (1): 115-149. 2020.This paper first investigates logical characterizations of different structures of opposition that extend the square of opposition in a way or in another. Blanché’s hexagon of opposition is based on three disjoint sets. There are at least two meaningful cubes of opposition, proposed respectively by two of the authors and by Moretti, and pioneered by philosophers such as J. N. Keynes, W. E. Johnson, for the former, and H. Reichenbach for the latter. These cubes exhibit four and six squares of opp…Read more
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28On Ignorance and Contradiction Considered as Truth-ValuesLogic Journal of the IGPL 16 (2): 195-216. 2008.A critical view of the alleged significance of Belnap four-valued logic for reasoning under inconsistent and incomplete information is provided. The difficulty lies in the confusion between truth-values and information states, when reasoning about Boolean propositions. So our critique is along the lines of previous debates on the relevance of many-valued logics and especially of the extension of the Boolean truth-tables to more than two values as a tool for reasoning about uncertainty. The criti…Read more
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3The first steps in fuzzy set theory in France forty years agoArchives for the Philosophy and History of Soft Computing 2017 (1). 2017.At the occasion of the fiftieth anniversary of the founding article “Fuzzy sets” by L. A. Zadeh, published in 1965, we briefly outline the beginnings of fuzzy set research in France, taking place some ten years later, pointing out the pioneer- ing role of Arnold Kaufmann and few others in this emergence. Moreover, we also point out that the French counterpart of the name “fuzzy set” had appeared some 15 years before Zadeh’s paper, in a paper written in French by the very person who also invented…Read more
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49On the relation between possibilistic logic and modal logics of belief and knowledgeJournal of Applied Non-Classical Logics 27 (3-4): 206-224. 2017.Possibilistic logic and modal logic are knowledge representation frameworks sharing some common features, such as the duality between possibility and necessity, and the decomposability of necessity for conjunctions, as well as some obvious differences since possibility theory is graded. At the semantic level, possibilistic logic relies on possibility distributions and modal logic on accessibility relations. In the last 30 years, there have been a series of attempts for bridging the two framework…Read more
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76Knowledge-driven versus data-driven logicsJournal of Logic, Language and Information 9 (1): 65--89. 2000.The starting point of this work is the gap between two distinct traditions in information engineering: knowledge representation and data - driven modelling. The first tradition emphasizes logic as a tool for representing beliefs held by an agent. The second tradition claims that the main source of knowledge is made of observed data, and generally does not use logic as a modelling tool. However, the emergence of fuzzy logic has blurred the boundaries between these two traditions by putting forwar…Read more
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10A glance at non-standard models and logics of uncertainty and vaguenessIn Anthony Eagle (ed.), Philosophy of Probability, Routledge. pp. 169--222. 1955.
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73A practical approach to revising prioritized knowledge basesStudia Logica 70 (1): 105-130. 2002.This paper investigates simple syntactic methods for revising prioritized belief bases, that are semantically meaningful in the frameworks of possibility theory and of Spohn''s ordinal conditional functions. Here, revising prioritized belief bases amounts to conditioning a distribution function on interpretations. The input information leading to the revision of a knowledge base can be sure or uncertain. Different types of scales for priorities are allowed: finite vs. infinite, numerical vs. ord…Read more
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60Suitable properties for any electronic voting systemArtificial Intelligence and Law 14 (4): 251-260. 2006.Numerous countries are heading toward digital infrastructures. In particular this new technology promises to help support methods for elections. However, one should be careful that such an infrastructure does not hinder the voting and representation issues. On the contrary, it should support those issues and help citizens have a clearer picture of the underlying mechanisms. This paper deals with the limits of voting procedures as they are described in classical collective choice theory and refle…Read more
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46Fuzzy Sets and Systems: Theory and ApplicationsAcademic Press. 1980./ Part INTRODUCTION Fuzziness is not a priori an obvious concept and demands some explanation. "Fuzziness" is what Black (NF) calls "vagueness" when ...
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190Three-valued logics for incomplete information and epistemic logicIn Luis Farinas del Cerro, Andreas Herzig & Jerome Mengin (eds.), Logics in Artificial Intelligence, Springer. pp. 147--159. 2012.
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93New Trends and Open Problems in Fuzzy Logic and Approximate ReasoningTheoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 11 (3): 109-121. 1996.This short paper about fuzzy set-based approximate reasoning first emphasizes the three main semantics for fuzzy sets: similarity, preference and uncertainty. The difference between truth-functional many-valued logics of vague or gradual propositions and non fully compositional calculi such as possibilistic logic or similarity logics is stressed. Then, potentials of fuzzy set-based reasoning methods are briefly outlined for various kinds of approximate reasoning: deductive reasoning about flexib…Read more
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18Author’s response to Wansing and Belnap’s Generalized truth-valuesLogic Journal of the IGPL 18 (6): 936-940. 2010.
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43Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study part 1: The flat caseStudia Logica 58 (1): 17-45. 1997.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 argumentati…Read more