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

International audienceThere 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

The *-composition -A Novel Generating Method of Fuzzy Implications: An Algebraic Study

Fuzzy implications are one of the two most important fuzzy logic connectives, the other being t-norms. They are a generalisation of the classical implication from two-valued logic to the multivalued setting. A binary operation I on [0; 1] is called a fuzzy implication if (i) I is decreasing in the first variable, (ii) I is increasing in the second variable, (iii) I(0; 0) = I(1; 1) = 1 and I(1; 0) = 0. The set of all fuzzy implications defined on [0; 1] is denoted by I. Fuzzy implications have many applications in fields like fuzzy control, approximate reasoning, decision making, multivalued logic, fuzzy image processing, etc. Their applicational value necessitates new ways of generating fuzzy implications that are fit for a specific task. The generating methods of fuzzy implications can be broadly categorised as in the following: (M1): From binary functions on [0; 1], typically other fuzzy logic connectives, viz., (S;N)-, R-, QL- implications, (M2): From unary functions on [0,1], typically monotonic functions, for instance, Yager’s f-, g- implications, or from fuzzy negations, (M3): From existing fuzzy implications

The ⊛-composition of fuzzy implications: Closures with respect to properties, powers and families

Recently, Vemuri and Jayaram proposed a novel method of generating fuzzy implications from a given pair of fuzzy implications. Viewing this as a binary operation ⊛ on the set II of fuzzy implications they obtained, for the first time, a monoid structure (I,⊛)(I,⊛) on the set II. Some algebraic aspects of (I,⊛)(I,⊛) had already been explored and hitherto unknown representation results for the Yager's families of fuzzy implications were obtained in [53] (N.R. Vemuri and B. Jayaram, Representations through a monoid on the set of fuzzy implications, fuzzy sets and systems, 247 (2014) 51–67). However, the properties of fuzzy implications generated or obtained using the ⊛-composition have not been explored. In this work, the preservation of the basic properties like neutrality, ordering and exchange principles , the functional equations that the obtained fuzzy implications satisfy, the powers w.r.t. ⊛ and their convergence, and the closures of some families of fuzzy implications w.r.t. the operation ⊛, specifically the families of (S,N)(S,N)-, R-, f- and g-implications, are studied. This study shows that the ⊛-composition carries over many of the desirable properties of the original fuzzy implications to the generated fuzzy implications and further, due to the associativity of the ⊛-composition one can obtain, often, infinitely many new fuzzy implications from a single fuzzy implication through self-composition w.r.t. the ⊛-composition

Aggregation of L-probabilistic quasi-uniformities

[EN] The problem of aggregating fuzzy structures, mainly fuzzy binary relations, has deserved a lot of attention in the last years due to its application in several fields. Here, we face the problem of studying which properties must satisfy a function in order to merge an arbitrary family of (bases of) L-probabilistic quasi-uniformities into a single one. These fuzzy structures are special filters of fuzzy binary relations. Hence we first make a complete study of functions between partially-ordered sets that preserve some special sets, such as filters. Afterwards, a complete characterization of those functions aggregating bases of L-probabilistic quasi-uniformities is obtained. In particular, attention is paid to the case L={0,1}, which allows one to obtain results for functions which aggregate crisp quasi-uniformities. Moreover, we provide some examples of our results including one showing that Lowen's functor iota which transforms a probabilistic quasi-uniformity into a crisp quasi-uniformity can be constructed using this aggregation procedure.J. Rodriguez-Lopez acknowledges financial support from FEDER/Ministerio de Ciencia, Innovacion y Universidades-Agencia Estatal de Investigacion Proyecto PGC2018-095709-B-C21.Pedraza Aguilera, T.; Rodríguez López, J. (2020). Aggregation of L-probabilistic quasi-uniformities. Mathematics. 8(11):1-21. https://doi.org/10.3390/math8111980S12181

Apertura e flessibilità nell'istruzione superiore: oltre l'e-learning? Atti del Convegno, Perugia, 13-14-15 Novembre 2014

Atti del Convegno SiremSiel2014 tenutosi a Perugia dal 13 al 14 novembre 2014: "Apertura e flessibilità nell'istruzione superiore: oltre l'e-learning?

Formalisation et exploitation de connaissances et d’expériences pour l’aide à la décision dans les processus d’ingénierie système

Ce manuscrit d’habilitation à diriger des recherche synthétise mon activité professionnelle en enseignement et en recherche depuis l’obtention de mon poste de maître de conférences en 2001. Après l’obtention de mon diplôme de doctorat, préparé au Laboratoire Génie de Production (LGP) entre 1997 et 2000 sous la direction de Bernard Grabot, j’ai obtenu mon poste de maître de conférences à l’Université de Bretagne Sud à Lorient (UBS). Durant une période de trois années dans cette université et au Laboratoire d’Electronique des Systèmes Temps Réels (LESTER devenu LAB-STICC par la suite), j’ai pu développer des activités de recherche dans le domaine de la conception et de la reconfiguration des systèmes automatisés de type Systèmes Transitiques. Suite à ma mutation à l’Ecole Nationale d’Ingénieurs de Tarbes en 2004, j’ai poursuivi mes activités de recherche au Laboratoire Génie de Production (LGP) en lien avec le développement d’outils d’aide ‘a la décision dans les processus d’ingénierie système basés sur l’exploitation de connaissances et d’expériences. En enseignement, depuis 2001, mes activités sont partagées entre le génie industriel et l’informatique. Ce document est structuré en deux parties : 1. la première partie permet d’exposer, dans mon Curriculum Vitae détaillé, un bilan de mes activités d’enseignant-chercheur. Mon parcours professionnel, mes activités d’enseignement et un bilan de mes activités de recherche sont exposés de manière synthétique. Dans un premier temps, les enseignements dont j’ai eu la responsabilité (conception et ou réalisation) ainsi que les documents pédagogiques produits et les volumes horaires sont exposés. Ensuite, les encadrements de chercheurs (doctorants, masters et post-doctorat), les projets institutionnels (FUI et ANR) dans lesquels j’ai pris des responsabilités, les partenariats avec des entreprises dans le cadre de contrats CIFRE, mes activités d’animation de la recherche au niveau national et international font partie de ce bilan. Cette section se termine par la liste exhaustive de mes publications et communications (section 3.5) réalisées depuis le début de mon activité de chercheur, en 1997, 2. la seconde partie synthétise mes activités de recherche réalisées depuis 2001. Cette seconde partie est présentée selon 6 chapitres. Le chapitre 1 permet d’exposer la problématique globale de mes travaux de recherche. Elle est orientée par un modèle à trois niveaux (Processus, Outils, Expériences / Connaissances) et étayée par un premier niveau d’étude bibliographique. Le niveau de détail choisi permet de comprendre cette problématique dans sa globalité. Les processus ciblés, les outils développés, les connaissances exploitées sont présentés au regard de la littérature dans les différents domaines. Les chapitres 2 à 5 fournissent quant à eux un niveau de détail plus fin. Ils permettent de présenter les problématiques de manière affinée, les développements réalisés et les contributions scientifiques majeures. L’objectif est de fournir des éléments qui soient utiles à la compréhension de mon activité de recherche mais, également, d’en favoriser l’exploitation ultérieure. Enfin, dans le chapitre 6, la conclusion permet de prendre le recul nécessaire au travaux réalisés et de proposer mon projet de recherche pour les années à venir

Safety and Reliability - Safe Societies in a Changing World

The contributions cover a wide range of methodologies and application areas for safety and reliability that contribute to safe societies in a changing world. These methodologies and applications include: - foundations of risk and reliability assessment and management - mathematical methods in reliability and safety - risk assessment - risk management - system reliability - uncertainty analysis - digitalization and big data - prognostics and system health management - occupational safety - accident and incident modeling - maintenance modeling and applications - simulation for safety and reliability analysis - dynamic risk and barrier management - organizational factors and safety culture - human factors and human reliability - resilience engineering - structural reliability - natural hazards - security - economic analysis in risk managemen

Talking About Uncertainty

In the first article we review existing theories of uncertainty. We devote particular attention to the relation between metacognition, uncertainty and probabilistic expectations. We also analyse the role of natural language and communication for the emergence and resolution of states of uncertainty. We hypothesize that agents feel uncertainty in relation to their levels of expected surprise, which depends on probabilistic expectations-gaps elicited during communication processes. Under this framework above tolerance levels of expected surprise can be considered informative signals. These signals can be used to coordinate, at the group and social level, processes of revision of probabilistic expectations. When above tolerance levels of uncertainty are explicated by agents through natural language, in communication networks and public information arenas, uncertainty acquires a systemic role of coordinating device for the revision of probabilistic expectations. The second article of this research seeks to empirically demonstrate that we can crowd source and aggregate decentralized signals of uncertainty, i.e. expected surprise, coming from market agents and civil society by using the web and more specifically Twitter as an information source that contains the wisdom of the crowds concerning the degree of uncertainty of targeted communities/groups of agents at a given moment in time. We extract and aggregate these signals to construct a set of civil society uncertainty proxies by country. We model the dependence among our civil society uncertainty indexes and existing policy and market uncertainty proxies, highlighting contagion channels and differences in their reactiveness to real-world events that occurred in the year 2016, like the EU-referendum vote and the US presidential elections. In the third article, we propose a new instrument, called Worldwide Uncertainty Network, to analyse the uncertainty contagion dynamics across time and areas of the world. Such an instrument can be used to identify the systemic importance of countries in terms of their civil society uncertainty social percolation role. Our results show that civil society uncertainty signals coming from the web may be fruitfully used to improve our understanding of uncertainty contagion and amplification mechanisms among countries and between markets, civil society and political systems