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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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8An 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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45Aggregation 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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17Fuzzy 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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5Special 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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10Nonmonotonic reasoning, conditional objects and possibility theoryArtificial Intelligence 92 (1-2): 259-276. 1997.
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3Special 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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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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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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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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13An 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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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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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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34Multiple 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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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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45Qualitative 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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78Knowledge-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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14A glance at non-standard models and logics of uncertainty and vaguenessIn Anthony Eagle (ed.), Philosophy of Probability, Routledge. pp. 169--222. 1955.