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192Three-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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94New 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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81Knowledge-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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74A 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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69From Blanché’s Hexagonal Organization of Concepts to Formal Concept Analysis and Possibility TheoryLogica Universalis 6 (1-2): 149-169. 2012.The paper first introduces a cube of opposition that associates the traditional square of opposition with the dual square obtained by Piaget’s reciprocation. It is then pointed out that Blanché’s extension of the square-of-opposition structure into an conceptual hexagonal structure always relies on an abstract tripartition. Considering quadripartitions leads to organize the 16 binary connectives into a regular tetrahedron. Lastly, the cube of opposition, once interpreted in modal terms, is shown…Read more
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61Suitable 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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56A 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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55On 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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48Fuzzy 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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46Qualitative Heuristics For Balancing the Pros and ConsTheory and Decision 65 (1): 71-95. 2008.Balancing the pros and cons of two options is undoubtedly a very appealing decision procedure, but one that has received scarce scientific attention so far, either formally or empirically. We describe a formal framework for pros and cons decisions, where the arguments under consideration can be of varying importance, but whose importance cannot be precisely quantified. We then define eight heuristics for balancing these pros and cons, and compare the predictions of these to the choices made by 6…Read more
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45Aggregation of decomposable measures with application to utility theoryTheory and Decision 41 (1): 59-95. 1996.
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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
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39The Strength of Desires: A Logical ApproachMinds and Machines 27 (1): 199-231. 2017.The aim of this paper is to propose a formal approach to reasoning about desires, understood as logical propositions which we would be pleased to make true, also acknowledging the fact that desire is a matter of degree. It is first shown that, at the static level, desires should satisfy certain principles that differ from those to which beliefs obey. In this sense, from a static perspective, the logic of desires is different from the logic of beliefs. While the accumulation of beliefs tend to re…Read more
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35Multiple agent possibilistic logicJournal of Applied Non-Classical Logics 23 (4): 299-320. 2013.The paper presents a ‘multiple agent’ logic where formulas are pairs of the form, made of a proposition and a subset of agents. The formula is intended to mean ‘ all agents in believe that is true’. The formal similarity of such formulas with those of possibilistic logic, where propositions are associated with certainty levels, is emphasised. However, the subsets of agents are organised in a Boolean lattice, while certainty levels belong to a totally ordered scale. The semantics of a set of ‘mul…Read more
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32On 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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21Inference in possibilistic hypergraphsIn B. Bouchon-Meunier, R. R. Yager & L. A. Zadeh (eds.), Uncertainty in Knowledge Bases, Springer. pp. 249--259. 1991.
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21Structures 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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18Author’s response to Wansing and Belnap’s Generalized truth-valuesLogic Journal of the IGPL 18 (6): 936-940. 2010.
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18Fuzzy set and possibility theory-based methods in artificial intelligenceArtificial Intelligence 148 (1-2): 1-9. 2003.
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15An overview of bipolar qualitative decision rulesIn Giacomo Della Riccia, Didier Dubois & Hans-Joachim Lenz (eds.), Preferences and Similarities, Springer. pp. 47--73. 2008.
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14A 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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13Accepted beliefs, revision and bipolarity in the possibilistic frameworkIn Franz Huber & Christoph Schmidt-Petri (eds.), Degrees of belief, Springer. pp. 161--184. 2009.
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11An 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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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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11Possibilistic reasoning with partially ordered beliefsJournal of Applied Logic 13 (4): 770-798. 2015.
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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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10Nonmonotonic reasoning, conditional objects and possibility theoryArtificial Intelligence 92 (1-2): 259-276. 1997.