Description du projet
Définir la représentation des connaissances vagues
Une logique se compose d’un langage formel ou informel, d’un système déductif décrivant les arguments valables pour le langage donné et d’une sémantique définissant la signification des composants du langage. La logique existe pour toutes sortes de langages, y compris les langages parlés et les langages de codage. Comme pour le langage humain, la logique mathématique peut être appelée à représenter des informations «vagues». Le raisonnement vague et la représentation des connaissances correspondantes sont des domaines qui ont d’importantes applications pratiques. Par exemple, la logique floue aborde le «raisonnement» avec des degrés de vérité au lieu des classiques vrai (1) et faux (0). Avec le soutien du programme Actions Marie Skłodowska-Curie, le projet ClaVa étudie les formes clausales dans les logiques non-classiques pour les utiliser dans le traitement des informations vagues.
Objectif
This is a resubmission of proposal number 898845 submitted to MSCA-IF-2019 and not funded.
The main objective of this project is to study clausal-form systems for real and rational-valued events, facing the questions of their general definition, usage and solvable problems (SAT and optimality) from the point of view of their complexity, algorithmic design and applicability. It is focused on studying in full generality the definition of clausal form in non-classical logics for their use in vague knowledge representation. At the most general level, it is planned to reach a the definition based on n-ary- level subsets of literals and using symmetric term-definable operations of arbitrary arity to combine each level, over Mathematical Fuzzy Logics and over some other Substructural Logics. In the first family of logics, vague concepts with inverse (tall-short, hot-cold, etc), truth stressers and comparaisons (more, much more, etc) can be modeled naturally. On the other hand, substructural logics allow to model non-linearly ordered notions (eg. situations that cannot be considered better or worse between them), and non-integral algebras for combination of knowledge (i.e. with an operation * such that x*y > x for some y). We plan to 1) introduce definitions of general clausal forms over the above logical systems, study their possible equivalences and their logical properties (axiomatization of fragments, admissible rules, etc); 2) study real-world vague notions to be modeled using some of the previous forms and of the above logics; 3) design and test efficient solving procedures for three natural questions: SAT (evaluation sending the clause to 1), Max-SAT (evaluation maximizing the number of satisfied clauses) and optimality with respect to an objective (evaluation maximizing/minimizing the clause) 4) do a complexity classification of the clausal forms, and study their normality (i.e. if any formula is equivalent to one in the desired form for the problems above).
Champ scientifique
Programme(s)
Régime de financement
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)Coordinateur
28006 Madrid
Espagne