Clausal forms for Vague information processing

Descripción del proyecto

Determinación de la representación del conocimiento impreciso

Una lógica consiste en un lenguaje formal o informal junto con un sistema deductivo que describe argumentos válidos para el lenguaje dado y una semántica que define los significados de los componentes del lenguaje. Existen lógicas para todo tipo de lenguajes, incluidos los lenguajes hablados y de programación. Al igual que con el lenguaje humano, se puede recurrir a la lógica matemática para representar información «vaga». El razonamiento ambiguo y la representación del conocimiento impreciso son ámbitos con importantes aplicaciones prácticas. Por ejemplo, la lógica difusa se acerca al «razonamiento» con grados de verdad en lugar de los clásicos verdadero (1) y falso (0). En el proyecto ClaVa, que cuenta con el apoyo de las Acciones Marie Skłodowska-Curie, se estudian cláusulas en lógicas no clásicas para su uso en el procesamiento de información vaga.

Objetivo

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).