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23 results on '"Dubois, D"'

1. Possibilistic reasoning from partially ordered belief bases with the sure thing principle

Author

Cayrol, C., Dubois, D., Fayçal Touazi, Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Centre National de la Recherche Scientifique (CNRS), Université M'Hamed Bougara Boumerdes (UMBB), Institut National Polytechnique de Toulouse - INPT (FRANCE), Centre National de la Recherche Scientifique - CNRS (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Université Toulouse - Jean Jaurès - UT2J (FRANCE), Université Toulouse 1 Capitole - UT1 (FRANCE), and Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)

Subjects
Possibility theory, Partially ordered bases, TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES, Computer Science::Logic in Computer Science, Comparative probability, Adjunction rule, Intelligence artificielle, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Abstract

International audience; We consider the problem of reasoning from logical bases equipped with a partial order expressing relative certainty, with a view to construct a partially ordered deduc-tive closure via syntactic inference. At the syntactic level we use a language expressing pairs of related formulas and axioms describing the properties of the order. Reasoning about uncertainty using possibility theory relies on the idea that if an agent believes each among two propositions to some extent, then this agent should believe their conjunction to the same extent. This principle is known as adjunction. Adjunction is often accepted in epistemic logic but fails with probabilistic reasoning. In the latter, another principle prevails, namely the sure thing principle, that claims that the certainty ordering between propositions should be invariant to the addition or deletion of possible worlds common to both sets of models of these propositions. Pursuing our work on relative certainty logic based on possibility theory, we propose a qualitative likelihood logic that respects the sure thing principle, albeit using a likelihood relation that preserves adjunction.

Published
2018

2. From a Possibility Theory View of Formal Concept Analysis to the Possibilistic Handling of Incomplete and Uncertain Contexts

Author

Ait-Yakoub, Z, Djouadi, Y, Dubois, D, Prade, H, Centre National de la Recherche Scientifique - CNRS (FRANCE), Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Université Toulouse - Jean Jaurès - UT2J (FRANCE), Université Toulouse 1 Capitole - UT1 (FRANCE), Université Mouloud Mammeri Tizi Ouzou - UMMTO (ALGERIA), Institut de Recherche en Informatique de Toulouse - IRIT (Toulouse, France), Université Mouloud Mammeri [Tizi Ouzou] (UMMTO), Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Centre National de la Recherche Scientifique (CNRS), Sergei O. Kuznetsov, Amedeo Napoli, Sebastian Rudolph, and Institut National Polytechnique de Toulouse - INPT (FRANCE)

Subjects
Logique en informatique, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Possibilistic operator, [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], Informatique et langage, Intelligence artificielle, [INFO.INFO-CL]Computer Science [cs]/Computation and Language [cs.CL], Apprentissage, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Abstract

© 2016, CEUR-WS. All rights reserved. The formal similarity between possibility theory and formal concept analysis, made ten years ago, has suggested the introduction in the latter setting of the counterpart of possibilistic operators, which were ignored before. These new operators can be related to the basic operator of formal concept analysis by a triple use of negations on the contexts, on the set-valued arguments and on the obtained results, and lead to consider new compositions worth of interest. They enable us to complete the Guigues-Duquenne basis with rules having disjunctive conclusions. Besides, the approach can be naturally generalized to incomplete contexts and then to uncertain context where uncertainty is graded.

Published
2016

3. A general framework for revising belief bases using qualitative jeffrey's rule

Author

Benferhat, S., Dubois, D., Prade, H., Mary-Anne Williams, Centre de Recherche en Informatique de Lens (CRIL), Université d'Artois (UA)-Centre National de la Recherche Scientifique (CNRS), Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, and Centre National de la Recherche Scientifique (CNRS)

Subjects
Artificial Intelligence & Image Processing, ComputingMilieux_MISCELLANEOUS, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Abstract

Intelligent agents require methods to revise their epistemic state as they acquire new information. Jeffrey's rule, which extends conditioning to uncertain inputs, is currently used for revising probabilistic epistemic states when new information is uncertain. This paper analyses the expressive power of two possibilistic counterparts of Jeffrey's rule for modeling belief revision in intelligent agents. We show that this rule can be used to recover most of the existing approaches proposed in knowledge base revision, such as adjustment, natural belief revision, drastic belief revision, revision of an epistemic by another epistemic state. In addition, we also show that that some recent forms of revision, namely improvement operators, can also be recovered in our framework. © 2009 Springer Berlin Heidelberg.

Published
2009

4. Possibility theory and formal concept analysis in information systems

Author

Dubois, D, Prade, H, Grélaud, Françoise, Carvalho, Joao Paulo, Dubois, Didier, Kaymak, Uzay, Sousa, Joao M.C, Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), and Université Fédérale Toulouse Midi-Pyrénées

Subjects
[INFO.INFO-AI] Computer Science [cs]/Artificial Intelligence [cs.AI], formal concept analysis, possibility theory, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Abstract

International audience; The setting of formal concept analysis presupposes the existence of a relation between objects and properties. Knowing that an unspecified object has a given property induces a formal possibil-ity distribution that models the set of objects known to possess this property. This view expressed in a recent work by the authors of the present paper, has led to introduce the set-valued counterpart to the four set functions evaluating potential or actual, possibility or neces-sity that underlie bipolar possibility theory, and to study associated notions. This framework puts formal concept analysis in a new, en-larged perspective, further explored in this article. The “actual (or guaranteed) possibility” function induces the usual Galois connex-ion that defines the notion of a concept as the pair of its extent and its intent. A new Galois connexion, based on the necessity measure, partitions the relation in “orthogonal” subsets of objects having dis-tinct properties. Besides, the formal similarity between the notion of division in relational algebra and the “actual possibility” function leads to define the fuzzy set of objects having most properties in a set, and other related notions induced by fuzzy extensions of division. Generally speaking, the possibilistic view of formal concept analysis still applies when properties are a matter of degree, as discussed in the paper. Lastly, cases where the object / property relation is incom-plete due to missing information, or more generally pervaded with possibilistic uncertainty is also discussed.

Published
2009

5. On various definitions of the variance of a fuzzy random variable

Author

Inés Couso, Dubois, D., Montes, S., Sánchez, L., Universidad de Oviedo [Oviedo], Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, grants MTM2004-01269 and TIC2002-04036-C05-05, De Cooman, Gert and and, Vejnarova, Jirina, Zaffalon, Marco, and Grélaud, Françoise

Subjects
[INFO.INFO-AI] Computer Science [cs]/Artificial Intelligence [cs.AI], Fuzzy random variable, random set, variance, second order possibility measure, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Abstract

D&al004; International audience; According to the current literature, there are two different approaches to the definition of the variance of a fuzzy random variable. In the first one, the variance is defined as a fuzzy interval, offering a gradual description of our incomplete knowledge about the variance of an underlying, imprecisely observed, classical random variable. In the second case, the variance of the fuzzy random variable is defined as a crisp number, that makes it easier to handle in further processing. In this work, we introduce yet another definition of the variance of a fuzzy random variable, in the context of the theory of imprecise probabilities. The new variance is not defined as a fuzzy or crisp number, but it is a real interval, which is a compromise between both previous definitions. Our main objectives are twofold: first, we show the interpretation of the new variance and, second, with the help of simple examples, we demonstrate the usefulness of all these definitions when applied to particular situations.

Published
2007

6. Background default knowledge and causality ascriptions

Author

Jean-François Bonnefon, Da Silva Neves, R., Dubois, D., Prade, H., Institut Jean-Nicod (IJN), Département d'Etudes Cognitives - ENS Paris (DEC), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École des hautes études en sciences sociales (EHESS)-Collège de France (CdF (institution))-Centre National de la Recherche Scientifique (CNRS)-Département de Philosophie - ENS Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), DynamiquesSociales et Vie Politique (DSVP), Université Toulouse - Jean Jaurès (UT2J), Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Centre National de la Recherche Scientifique (CNRS), European Coordinating Committee for Artificial Intelligence (ECCAI), Italian Association of Artificial Intelligence, Gerhard Brewka, Silvia Coradeschi, Anna Perini, Paolo Traverso, and Grélaud, Françoise

Subjects
[INFO.INFO-AI] Computer Science [cs]/Artificial Intelligence [cs.AI], [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Abstract

International audience; A model is defined that predicts an agent’s ascriptions of causality (and related notions of facilitation and justification) between two events in a chain, based on background knowledge about the normal course of the world. Background knowledge is represented by nonmonotonic consequence relations. This enables the model to handle situations of poor information, where background knowledge is not accurate enough to be represented in, e.g., structural equations. Tentative properties of causality ascriptions are explored, i.e., preference for abnormal factors, transitivity, coherence with logical entailment, and stability with respect to disjunction and conjunction. Empirical data are reported to support the psychological plausibility of our basic definitions.

Published
2006

7. Probabilities of events induced by fuzzy random variables

Author

Baudrit, C., Inés Couso, Dubois, D., Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Universidad de Oviedo [Oviedo], Spanish project MTM2004-01269, and Centre National de la Recherche Scientifique (CNRS)

Subjects
Possibility measure, fuzzy random variable, [SDV]Life Sciences [q-bio], random set, ComputingMilieux_MISCELLANEOUS, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Abstract

BaudD&al001; International audience; Propagating possibilistic and probabilistic variables through a mapping yields a fuzzy random variable. We propose a method to attach probability intervals to events pertaining to the output variable. We show that this method is consistent with classical approaches to fuzzy random variables and that the obtained probability interval is the mean value of the fuzzy probability defined by viewing a fuzzy random variable as higher order possibilistic uncertainty.

Published
2005

8. Minimizing a makespan under uncertainty

Author

Fortin, J., Pawel Zielinski, Dubois, D., Fargier, H., Laboratoire de géologie de l'ENS (LGENS), Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS)-Département des Géosciences - ENS Paris, École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Uniwersytet Wroclawski, and International Joint Conferences on Artificial Intelligence

Subjects
[INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Abstract

DFargFort&al002; International audience; This paper reconsiders the most basic scheduling problem, that of minimizing the makespan of a partially ordered set of activities, in the context of incomplete knowledge. After positioning this paper in the scope of temporal networks under uncertainty, we provide a complete solution to the problem of finding floats of activities, and of locating surely critical ones, as they are often isolated. The minimal float problem is NP-hard while the maximal float problem is polynomial. New complexity results and efficient algorithms are provided for the interval-valued makespan minimization problem.

Published
2005

9. A practical approach to revising prioritized knowledge bases

Author

Benferhat, S., Dubois, D., Prade, H., Mary-Anne Williams, DELORME, Fabien, Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Quantum Computation & Intelligent Systems [Ultimo] (UTS:QCIS), and University of Technology Sydney (UTS)

Subjects
[INFO.INFO-AI] Computer Science [cs]/Artificial Intelligence [cs.AI], General Mathematics, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Abstract

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. ordinal. Syntactic revision is envisaged here as a process which transforms a prioritized belief bases into a new prioritized belief base, and thus allows a subsequent iteration. © 2002 Kluwer Academic Publishers.

Published
2002

10. Un problème de satisfaction de contraintes flexibles en oenologie

Author

Régis Sabbadin, Dubois, D., Prade, H., Grenier, P., Irstea Publications, Migration, Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Génie instrumental qualité alimentaire (UR GIMO), and Centre national du machinisme agricole, du génie rural, des eaux et forêts (CEMAGREF)

Subjects
[SDE] Environmental Sciences, [INFO.INFO-AI] Computer Science [cs]/Artificial Intelligence [cs.AI], CEMAGREF, [SDE]Environmental Sciences, IRIT, GIMO, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Abstract

This paper reports on a real case study coming from wine industry, which is an example of linear constraint satisfaction problem, where the constraints are flexible, may have different levels of priority or involve ill-known (imprecise or fuzzy) parameters. Fuzzy sets and possibility theory offer a unified framework that allows for the modelling of i) preferences between different ways of satisfying a flexible constraint, of ii) uncertainty pervading data, and of iii) priority among constraints. Indeed, actual constraints are often flexible and their satisfaction a matter of degree. That is why they are conveniently described as fuzzy sets. Uncertain pieces of data can be represented by means of possibility distributions, and the level of priority of a constraint can be viewed as the maximum degree of acceptability of a solution that violates this constraint. In the following, the fuzzy set-based approach to the handling of soft and uncertain constraints is presented and its interest is illustrated on the case study., Cette publication présente une situation réelle en oenologie, qui correspond à un cas de satisfaction de contraintes linéaires, où les contraintes sont flexibles, peuvent prendre divers niveaux de priorité ou mettent en jeu des connaissances imparfaites (imprécises ou floues). Les nombres flous et la théorie des possibilités offrent un cadre unifié de représentation qui permet de modéliser : i) des préférences entre manières de satisfaire des contraintes flexibles, ii) la propagation de l'incertitude et iii) les priorités entre contraintes. Les contraintes dans la réalité sont souvent flexibles et leur satisfaction peut être estimée par des degrés. C'est pourquoi elles sont décrites naturellement par des ensembles flous. Des éléments de connaissances incertaines peuvent être représentés au moyen de distributions de possibilités, et leur niveau de priorité peut être vu comme le degré maximal d'acceptabilité d'une solution qui violerait la contrainte considérée. Dans la suite de la publication, une approche de gestion de contraintes flexibles et incertaines est présentée sur la base de d'ensembles flous, et son intérêt est illustré par le cas d'étude.

Published
1998

11. Extending answer set programming using generalized possibilistic logic

Author

Dubois, D, Prade, H, Schockaert, S, Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Centre National de la Recherche Scientifique (CNRS), Cardiff University, Centre National de la Recherche Scientifique - CNRS (FRANCE), Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Université Toulouse - Jean Jaurès - UT2J (FRANCE), Université Toulouse 1 Capitole - UT1 (FRANCE), Cardiff University (UNITED KINGDOM), and Institut National Polytechnique de Toulouse - INPT (FRANCE)

Subjects
Logique en informatique, QA75, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Logic, [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], Informatique et langage, Intelligence artificielle, Apprentissage, [INFO.INFO-CL]Computer Science [cs]/Computation and Language [cs.CL], [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Abstract

This international workshop is one of the joint ontology workshops JOWO 2015 affiliated with the 24th International Joint Conference on Artificial Intelligence (IJCAI-2015); International audience; Answer set programming (ASP) is a form of logic programming in which negation-as-failure is defined in a purely declarative way, based on the notion of a stable model. This short paper briefly explains how a recent generalization of possibilistic logic (GPL) can be used to characterize the semantics of answer set programming. This characterization has several advantages over existing characterizations of the stable model semantics. First, unlike reduct-based approaches, it does not rely on a syntactic procedure: we can directly characterize answer sets based on the minimally specific models of a GPL theory. Second, GPL enables us to study extensions of ASP in an intuitive way: unlike in existing generalizations of ASP such as equilibrium logic and autoepistemic logic, all formulas in GPL have a meaning which is intuitively clear. Finally, being based on possibilistic logic, GPL offers a natural way of dealing with uncertainty in answer set programs.

12. Structures of opposition induced by relations

Author

Didier Dubois, Davide Ciucci, Henri Prade, Centre National de la Recherche Scientifique - CNRS (FRANCE), Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Université Toulouse - Jean Jaurès - UT2J (FRANCE), Université Toulouse 1 Capitole - UT1 (FRANCE), Università degli Studi di Milano-Bicocca - BICOCCA (ITALY), Institut de Recherche en Informatique de Toulouse - IRIT (Toulouse, France), Ciucci, D, Dubois, D, Prade, H, Dipartimento di Informatica Sistemistica e Comunicazione (DISCo), Università degli Studi di Milano-Bicocca [Milano] (UNIMIB), Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Centre National de la Recherche Scientifique (CNRS), and Institut National Polytechnique de Toulouse - INPT (FRANCE)

Subjects
Square of opposition, Opposition (politics), 02 engineering and technology, Fuzzy relation, 01 natural sciences, Fuzzy logic, [INFO.INFO-CL]Computer Science [cs]/Computation and Language [cs.CL], [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Artificial Intelligence, 0202 electrical engineering, electronic engineering, information engineering, Formal concept analysis, Artificial Intelligence & Image Processing, 0101 mathematics, Composition of relations, Possibility theory, Mathematics, Logique en informatique, Multiple-valued logic, Binary relation, business.industry, Applied Mathematics, 010102 general mathematics, [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], INF/01 - INFORMATICA, Informatique et langage, Intelligence artificielle, 16. Peace & justice, Apprentissage, Algebra, Composition of relation, 020201 artificial intelligence & image processing, Rough set, Artificial intelligence, business
Abstract

© 2015, Springer International Publishing Switzerland. The paper shows that a cube of opposition, a structure that generalizes the square of opposition invented in ancient logic, can be generated from the composition of a binary relation with a subset, by the effect of set complementation on the subset, on the relation, or on the result of the composition. Since the composition of relations is encountered in many areas, the structure of opposition exhibited by the cube of opposition has a universal flavor. In particular, it applies to information processing-oriented settings such as rough set theory, possibility theory, or formal concept analysis. We then discuss how this structure extends to a fuzzy relation and a fuzzy subset, and the graded cube of opposition thus obtained provides an organized view of the different existing compositions of fuzzy relations. The paper concludes by pointing out areas of research where the cube of opposition, or its graded version are of interest.

Published
2015
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13. Algebraic models of deviant modal operators based on de Morgan and Kleene lattices

Author

Gianpiero Cattaneo, Didier Dubois, Davide Ciucci, Università degli Studi di Milano [Milano] (UNIMI), Dipartimento di Informatica Sistemistica e Comunicazione (DISCo), Università degli Studi di Milano-Bicocca [Milano] (UNIMIB), Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Queen's University [Belfast] (QUB), Cattaneo, G, Ciucci, D, and Dubois, D

Subjects
Pure mathematics, Kleene lattices, Information Systems and Management, Normal modal logic, Brouwer Zadeh lattices, 02 engineering and technology, Modal operator, 01 natural sciences, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], Theoretical Computer Science, Algebraic semantic of modal logic, symbols.namesake, Artificial Intelligence, Computer Science::Logic in Computer Science, 0202 electrical engineering, electronic engineering, information engineering, Abstract algebraic logic, 0101 mathematics, Fuzzy sets and orthopairs models, Mathematics, Heyting–Wajsberg algebras, Two-element Boolean algebra, 010102 general mathematics, Multimodal logic, Modal logic, rough sets, Brouwer Zadeh lattice, Kleene lattice, Heyting–Wajsberg algebra, Fuzzy sets, INF/01 - INFORMATICA, Modal logic, De Morgan's laws, Computer Science Applications, Interior algebra, Control and Systems Engineering, symbols, 020201 artificial intelligence & image processing, Software
Abstract

DCiucCatt001; International audience; An algebraic model of a kind of modal extension of de Morgan logic is described under the name MDS5 algebra. The main properties of this algebra can be summarized as follows: (1) it is based on a de Morgan lattice, rather than a Boolean algebra; (2) a modal necessity operator that satisfies the axioms N, K, T, and 5 (and as a consequence also B and 4) of modal logic is introduced; it allows one to introduce a modal possibility by the usual combination of necessity operation and de Morgan negation; (3) the necessity operator satisfies a distributivity principle over joins. The latter property cannot be meaningfully added to the standard Boolean algebraic models of S5 modal logic, since in this Boolean context both modalities collapse in the identity mapping. The consistency of this algebraic model is proved, showing that usual fuzzy set theory on a universe U can be equipped with a MDS5 structure that satisfies all the above points (1)–(3), without the trivialization of the modalities to the identity mapping. Further, the relationship between this new algebra and Heyting-Wajsberg algebras is investigated. Finally, the question of the role of these deviant modalities, as opposed to the usual non-distributive ones, in the scope of knowledge representation and approximation spaces is discussed.

Published
2011
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14. Structures of opposition in fuzzy rough sets

Author

Davide Ciucci, Henri Prade, Didier Dubois, Ciucci, D, Dubois, D, Prade, H, Centre National de la Recherche Scientifique - CNRS (FRANCE), Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Université Toulouse - Jean Jaurès - UT2J (FRANCE), Université Toulouse 1 Capitole - UT1 (FRANCE), Università degli Studi di Milano-Bicocca - BICOCCA (ITALY), Institut de Recherche en Informatique de Toulouse - IRIT (Toulouse, France), Dipartimento di Informatica Sistemistica e Comunicazione (DISCo), Università degli Studi di Milano-Bicocca [Milano] (UNIMIB), Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), and Université Fédérale Toulouse Midi-Pyrénées

Subjects
Square of opposition, Fuzzy set, Opposition (politics), 02 engineering and technology, Fuzzy relation, 01 natural sciences, [INFO.INFO-CL]Computer Science [cs]/Computation and Language [cs.CL], [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], Theoretical Computer Science, Computation Theory & Mathematics, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics, Fuzzy rough sets, Mathematics, Logique en informatique, Algebra and Number Theory, business.industry, Hexagonal crystal system, 010102 general mathematics, [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], Informatique et langage, Intelligence artificielle, 16. Peace & justice, square of opposition, fuzzy set, fuzzy relation, rough set, Apprentissage, Algebra, Computational Theory and Mathematics, Rough set, 020201 artificial intelligence & image processing, Artificial intelligence, business, Information Systems
Abstract

International audience; The square of opposition is as old as logic. There has been a recent renewal of interest on this topic, due to the emergence of new structures (hexagonal and cubic) extending the square. They apply to a large variety of representation frameworks, all based on the notions of sets and relations. After a reminder about the structures of opposition, and an introduction to their gradual extensions (exempli_ed on fuzzy sets), the paper more particularly studies fuzzy rough sets and rough fuzzy sets in the setting of gradual structures of opposition.

Published
2015
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15. Borderline vs. unknown: comparing three-valued representations of imperfect information

Author

Didier Dubois, Jonathan Lawry, Davide Ciucci, Università di Milano - Bicocca, Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées, Centre National de la Recherche Scientifique - CNRS (FRANCE), Institut National Polytechnique de Toulouse - INPT (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Université Toulouse - Jean Jaurès - UT2J (FRANCE), Université Toulouse 1 Capitole - UT1 (FRANCE), University of Bristol (UNITED KINGDOM), Università degli Studi di Milano-Bicocca - BICOCCA (ITALY), Institut de Recherche en Informatique de Toulouse - IRIT (Toulouse, France), Università degli Studi di Milano-Bicocca [Milano] (UNIMIB), Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Centre National de la Recherche Scientifique (CNRS), Ciucci, D, Dubois, D, Lawry, J, and Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)

Subjects
Theoretical computer science, Computer science, Vaguene, Expressive power, [INFO.INFO-CL]Computer Science [cs]/Computation and Language [cs.CL], Theoretical Computer Science, Supervaluations, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], Belnap logic, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Artificial Intelligence, Complete information, Representation (mathematics), Valuation (finance), Logique en informatique, Point (typography), business.industry, Applied Mathematics, INF/01 - INFORMATICA, [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], Informatique et langage, Vagueness, Intelligence artificielle, Rotation formalisms in three dimensions, Apprentissage, Partial models, Partial model, Kleene logic, Orthopair, Artificial intelligence, Imperfect, Orthopairs, business, Software, Incomplete information
Abstract

In this paper we compare the expressive power of elementary representation formats for vague, incomplete or conflicting information. These include Boolean valuation pairs introduced by Lawry and Gonzalez-Rodriguez, orthopairs of sets of variables, Boolean possibility and necessity measures, three-valued valuations, supervaluations. We make explicit their connections with strong Kleene logic and with Belnap logic of conflicting information. The formal similarities between 3-valued approaches to vagueness and formalisms that handle incomplete information often lead to a confusion between degrees of truth and degrees of uncertainty. Yet there are important differences that appear at the interpretive level: while truth-functional logics of vagueness are accepted by a part of the scientific community (even if questioned by supervaluationists), the truth-functionality assumption of three-valued calculi for handling incomplete information looks questionable, compared to the non-truth-functional approaches based on Boolean possibility-necessity pairs. This paper aims to clarify the similarities and differences between the two situations. We also study to what extent operations for comparing and merging information items in the form of orthopairs can be expressed by means of operations on valuation pairs, three-valued valuations and underlying possibility distributions. We explore the connections between several representations of imperfect information.In each case we compare the expressive power of these formalisms.In each case we study how to express aggregation operations.We demonstrate the formal similarities among these approaches.We point out the differences in interpretations between these approaches.

Published
2014
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16. The Structure of Oppositions in Rough Set Theory and Formal Concept Analysis - Toward a New Bridge between the Two Settings

Author

Henri Prade, Davide Ciucci, Didier Dubois, Centre National de la Recherche Scientifique - CNRS (FRANCE), Institut National Polytechnique de Toulouse - INPT (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Université Toulouse - Jean Jaurès - UT2J (FRANCE), Université Toulouse 1 Capitole - UT1 (FRANCE), Università degli Studi di Milano-Bicocca - BICOCCA (ITALY), Institut de Recherche en Informatique de Toulouse - IRIT (Toulouse, France), Dipartimento di Informatica Sistemistica e Comunicazione (DISCo), Università degli Studi di Milano-Bicocca [Milano] (UNIMIB), Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE), Beierle, C, Meghini, C, Ciucci, D, Dubois, D, and Prade, H

Subjects
Relation (database), Computer Science::Artificial Intelligence, [INFO.INFO-CL]Computer Science [cs]/Computation and Language [cs.CL], [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], Image (mathematics), Set (abstract data type), symbols.namesake, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Formal concept analysis, Artificial Intelligence & Image Processing, Mathematics, Structure (mathematical logic), Discrete mathematics, Logique en informatique, Possibility theory, Binary relation, Formal Concept Analysi, [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], Informatique et langage, Square of oppositions, Cartesian product, Intelligence artificielle, Apprentissage, Rough set, symbols
Abstract

Rough set theory (RST) and formal concept analysis (FCA) are two formal settings in information management, which have found applications in learning and in data mining. Both rely on a binary relation. FCA starts with a formal context, which is a relation linking a set of objects with their properties. Besides, a rough set is a pair of lower and upper approximations of a set of objects induced by an indistinguishability relation; in the simplest case, this relation expresses that two objects are indistinguishable because their known properties are exactly the same. It has been recently noticed, with different concerns, that any binary relation on a Cartesian product of two possibly equal sets induces a cube of oppositions, which extends the classical Aristotelian square of oppositions structure, and has remarkable properties. Indeed, a relation applied to a given subset gives birth to four subsets, and to their complements, that can be organized into a cube. These four subsets are nothing but the usual image of the subset by the relation, together with similar expressions where the subset and / or the relation are replaced by their complements. The eight subsets corresponding to the vertices of the cube can receive remarkable interpretations, both in the RST and the FCA settings. One facet of the cube corresponds to the core of RST, while basic FCA operators are found on another facet. The proposed approach both provides an extended view of RST and FCA, and suggests a unified view of both of them. © 2014 Springer International Publishing.

Published
2014
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17. A map of dependencies among three-valued logics

Author

Didier Dubois, Davide Ciucci, Dipartimento di Informatica Sistemistica e Comunicazione (DISCo), Università degli Studi di Milano-Bicocca [Milano] (UNIMIB), Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Centre National de la Recherche Scientifique (CNRS), Ciucci, D, Dubois, D, Centre National de la Recherche Scientifique - CNRS (FRANCE), Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Université Toulouse - Jean Jaurès - UT2J (FRANCE), Université Toulouse 1 Capitole - UT1 (FRANCE), Università degli Studi di Milano-Bicocca - BICOCCA (ITALY), Institut de Recherche en Informatique de Toulouse - IRIT (Toulouse, France), and Institut National Polytechnique de Toulouse - INPT (FRANCE)

Subjects
Information Systems and Management, Theoretical computer science, Functional completeness, 02 engineering and technology, Three-Valued Logic, 01 natural sciences, Logical connective, [INFO.INFO-CL]Computer Science [cs]/Computation and Language [cs.CL], Theoretical Computer Science, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], Meaning (philosophy of language), Negation, Fragment (logic), [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Artificial Intelligence, Truth value, 0202 electrical engineering, electronic engineering, information engineering, Functional Completeness, 0101 mathematics, Functional completene, Mathematics, Logique en informatique, Truth-Table, Point (typography), business.industry, 010102 general mathematics, INF/01 - INFORMATICA, [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], Informatique et langage, Intelligence artificielle, MV-Algebra, Apprentissage, Computer Science Applications, Control and Systems Engineering, 020201 artificial intelligence & image processing, Artificial intelligence, T-norm fuzzy logics, business, Software
Abstract

International audience; Three-valued logics arise in several fields of computer science, both inspired by concrete problems (such as in the management of the null value in databases) and theoretical considerations. Several three-valued logics have been defined. They differ by their choice of basic connectives, hence also from a syntactic and proof-theoretic point of view. Different interpretations of the third truth value have also been suggested. They often carry an epistemic flavor. In this work, relationships between logical connectives on three-valued functions are explored. Existing theorems of functional completeness have laid bare some of these links, based on specific connectives. However we try to draw a map of such relationships between conjunctions, negations and implications that extend Boolean ones. It turns out that all reasonable connectives can be defined from a few of them and so all known three-valued logics appear as a fragment of only one logic. These results can be instrumental when choosing, for each application context, the appropriate fragment where the basic connectives make full sense, based on the appropriate meaning of the third truth-value.

Published
2013
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18. From paraconsistent three-valued logics to multiple-source epistemic logic

Author

Davide Ciucci, Didier Dubois, Centre National de la Recherche Scientifique - CNRS (FRANCE), Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Université Toulouse - Jean Jaurès - UT2J (FRANCE), Université Toulouse 1 Capitole - UT1 (FRANCE), Università degli Studi di Milano-Bicocca - BICOCCA (ITALY), Institut de Recherche en Informatique de Toulouse - IRIT (Toulouse, France), Dipartimento di Informatica Sistemistica e Comunicazione (DISCo), Università degli Studi di Milano-Bicocca [Milano] (UNIMIB), Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Centre National de la Recherche Scientifique (CNRS), Pasi, G., Montero, J., Ciucci, D., Dubois, D, Ciucci, D, and Institut National Polytechnique de Toulouse - INPT (FRANCE)

Subjects
Logic, 02 engineering and technology, 01 natural sciences, [INFO.INFO-CL]Computer Science [cs]/Computation and Language [cs.CL], paraconsistent logic, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], Epistemic modal logic, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Monoidal t-norm logic, Truth value, 0202 electrical engineering, electronic engineering, information engineering, Calculus, 0101 mathematics, Principle of bivalence, Mathematics, Logique en informatique, epistemic logic, business.industry, 010102 general mathematics, INF/01 - INFORMATICA, Paraconsistent logic, Modal logic, [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], Informatique et langage, Intelligence artificielle, 16. Peace & justice, Apprentissage, 020201 artificial intelligence & image processing, Artificial intelligence, T-norm fuzzy logics, business, Principle of explosion, multiple source system
Abstract

National audience; Several interpretations can be given to the third truth value in three-valued logics. Here, we consider the case when it refers to the epistemic notion of contradictory, or both true and false at the same time. We study several paraconsistent three-valued logics that carry this concern and show that they can be translated into a fragment of a simple epistemic logic where modalities can only appear in front of literals. This logic is unusual in the sense that necessity modalities distribute over disjunctions instead of conjunctions. An equivalent translation into a fragment of KD modal logic can be obtained by exchanging the role of possibility and necessity modalities, highlighting the perfect symmetry between three-valued logics of contradiction and three-valued logics of incomplete information.

Published
2013

19. A modal theorem-preserving translation of a class of three-valued logics of incomplete information

Author

Didier Dubois, Davide Ciucci, Centre National de la Recherche Scientifique - CNRS (FRANCE), Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE), Université Toulouse III - Paul Sabatier - UT3 (FRANCE), Université Toulouse - Jean Jaurès - UT2J (FRANCE), Université Toulouse 1 Capitole - UT1 (FRANCE), Università degli Studi di Milano-Bicocca - BICOCCA (ITALY), Institut de Recherche en Informatique de Toulouse - IRIT (Toulouse, France), Dipartimento di Informatica Sistemistica e Comunicazione (DISCo), Università degli Studi di Milano-Bicocca [Milano] (UNIMIB), Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Ciucci, D, Dubois, D, and Institut National Polytechnique de Toulouse - INPT (FRANCE)

Subjects
Logic, Normal modal logic, Modal Logic, 02 engineering and technology, 01 natural sciences, [INFO.INFO-CL]Computer Science [cs]/Computation and Language [cs.CL], [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], three-valued logic, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Monoidal t-norm logic, 0202 electrical engineering, electronic engineering, information engineering, Accessibility relation, Calculus, 0101 mathematics, Mathematics, Discrete mathematics, Logique en informatique, Incomplete Information, 010102 general mathematics, Classical logic, Uncertainty, INF/01 - INFORMATICA, Modal logic, [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], Informatique et langage, Intelligence artificielle, Apprentissage, Three-Valued Logics, Philosophy, TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES, Many-valued logic, 020201 artificial intelligence & image processing, Kripke semantics, T-norm fuzzy logics
Abstract

International audience; 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 three-valued logics can be translated into KD as a modal formula of depth 1, with modalities in front of literals only, while preserving all tautologies and inference rules of the original three-valued logic. This simple information logic is a two-tiered classical propositional logic with simple semantics in terms of epistemic states understood as subsets of classical interpretations. We study in particular the translations of Kleene, Gödel, ᴌukasiewicz and Nelson logics. We show that Priest’s logic of paradox, closely connected to Kleene’s, can also be translated into our modal setting, simply by exchanging the modalities possible and necessary. Our work enables the precise expressive power of three-valued logics to be laid bare for the purpose of uncertainty management.

Published
2013
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20. Oppositions in rough set theory

Author

Davide Ciucci, Didier Dubois, Henri Prade, Li, T, Nguyen, HS, Wang, G, Grzymala-Busse, J, Janicki, R, Hassanien, AE, Yu, H, Ciucci, D, Dubois, D, Prade, H, Dipartimento di Informatica Sistemistica e Comunicazione (DISCo), Università degli Studi di Milano-Bicocca [Milano] (UNIMIB), Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Queen's University [Belfast] (QUB), FP7-Marie Curie Action (IEF) n.276158, and Li, Tian-rui

Subjects
Pure mathematics, Square of opposition, Paraconsistent logic, INF/01 - INFORMATICA, 0102 computer and information sciences, 02 engineering and technology, 16. Peace & justice, 01 natural sciences, Square (algebra), [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], 010201 computation theory & mathematics, Rough Set, 0202 electrical engineering, electronic engineering, information engineering, Tetrahedron, Calculus, Formal concept analysis, 020201 artificial intelligence & image processing, Artificial Intelligence & Image Processing, Rough set, Mathematics, Possibility theory, Variable precision
Abstract

International audience; The role of opposition in rough set theory is laid bare. There are two sources which generate oppositions in rough sets: approximations and relations. In the former case, we outline a hexagon and a cube of oppositions. In the second case, we define a classical square of oppositions and also a tetrahedron when considering the standpoint of two agents.

Published
2012
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21. Three-Valued Logics for Incomplete Information and Epistemic Logic

Author

Didier Dubois, Davide Ciucci, Ciucci, D, Dubois, D, Dipartimento di Informatica Sistemistica e Comunicazione (DISCo), Università degli Studi di Milano-Bicocca [Milano] (UNIMIB), Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Queen's University [Belfast] (QUB), FP7-Marie Curie Action (IEF) n° 276158, Luis Fariñas del Cerro, Andreas Herzig, and Jérôme Mengin

Subjects
Discrete mathematics, 010102 general mathematics, Truth table, Modal logic, INF/01 - INFORMATICA, 02 engineering and technology, three-valued logics, epistemic login, unknown, 16. Peace & justice, Propositional calculus, 01 natural sciences, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], Epistemic modal logic, Truth value, Monoidal t-norm logic, 0202 electrical engineering, electronic engineering, information engineering, Calculus, 020201 artificial intelligence & image processing, 0101 mathematics, T-norm fuzzy logics, Łukasiewicz logic, Mathematics
Abstract

International audience; There are several three-valued logical systems. They give the impression of a scattered landscape. The majority of the works on this subject gives the truth tables, sometimes an Hilbert style axiomatization in a basic propositional language and a completeness theorem with respect to those truth tables. We show that all the reasonable connectives in three-valued logics can be built starting from few of them. Nevertheless, the issue of the usefulness of each system in relation with the third truth value is often neglected. Here, we review the interpretations of the third truth value. Then, we focus on the unknown case, suggested by Kleene. We show that any formula in three-valued logics can be encoded as a fragment of an epistemic logic (formulae of modal depth 1, with modalities in front of literals), preserving all tautologies and inference rules. We study in particular, the translation of Kleene, Gödel, Łukasiewicz and Nelson logics. This work enables us to lay bare the limited expressive power of three-valued logics in uncertainty management.

Published
2012
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22. Relationships between Connectives in Three-Valued Logics

Author

Didier Dubois, Davide Ciucci, Dipartimento di Informatica Sistemistica e Comunicazione (DISCo), Università degli Studi di Milano-Bicocca [Milano] (UNIMIB), Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Queen's University [Belfast] (QUB), Salvatore Greco, Bernadette Bouchon-Meunier, Giulianella Coletti, Mario Fedrizzi, Benedetto Matarazzo, Ronald R. Yager, Greco, S, Bouchon-Meunier, B, Coletti, G, Fedrizzi, M, Matarazzo, B, Yager, R, Ciucci, D, and Dubois, D

Subjects
Interpretation (logic), Point (typography), Computer science, Logical operations, 010102 general mathematics, INF/01 - INFORMATICA, 02 engineering and technology, 16. Peace & justice, 01 natural sciences, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], Epistemology, Range (mathematics), Three-valued logic, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, 0101 mathematics, uncertainty, Value (mathematics)
Abstract

International audience; In the literature, several 3-valued logics can be found. They differ from a syntactic and proof-theoretic point of view as well as on the interpretation given to the third value, which, nevertheless, often assumes an epistemic flavor. This paper is a preliminary step in the attempt to clarify the situation of three-valued logics from a semantic point of view. Logical operations on three-valued functions are studied and their relationships put forward. They are also linked to existing logics, pointing out their usage and interpretation of the third value. In the long range, the idea is to be able to relate as many three-valued calculi as possible to classes of applications where the third truth-value is naturally interpreted, and the basic connectives make full sense.

Published
2012
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23. Truth-functionality, rough sets and three-valued logics

Author

Davide Ciucci, Didier Dubois, Dipartimento di Informatica Sistemistica e Comunicazione (DISCo), Università degli Studi di Milano-Bicocca [Milano] (UNIMIB), Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Multiple-Valued Logic Technical Committee of the IEEE Computer Society, Manyà, Felip, Esteva, Francesc, Gispert, Joan, Ciucci, D, and Dubois, D

Subjects
Discrete mathematics, Theoretical computer science, Three valued logics, rough sets, connectives, Fuzzy set, three-valued logics, INF/01 - INFORMATICA, Context (language use), 0102 computer and information sciences, 02 engineering and technology, Disjoint sets, Rough sets, 16. Peace & justice, Semantics, 01 natural sciences, truth functionality, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], 010201 computation theory & mathematics, Monoidal t-norm logic, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Relevance (information retrieval), Rough set, T-norm fuzzy logics, uncertainty, Mathematics
Abstract

DCiuc001; International audience; This paper investigates the significance of truthfunctional three valued logics of ill-known sets described by pairs of disjoint (or pairs of nested) subsets. In particular the case of three-valued logics of rough sets is studied in more details, showing that, while the mathematical underpinnings are sound, the relevance of these logics for reasoning about data-tables containing incomplete descriptions of objects is questionable.

Published
2010
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