Analyzing Natural-Language Knowledge Under Uncertainty on the Basis of Description Logics

The article overviews the means for describing and formally analyzing natural-language text knowledge under uncertainty. We consider a family of classic attribute languages and logics based on them, their properties, problems, and solution tools. We also overview propositional n-valued logics and fuzzy logics, their syntax and semantics. Based on the considered logical constructions, we propose syntax and set-theoretic interpretation of n-valued description logic ALCQ_n that provides the means for describing concept intersection, union, complement, value restrictions, and qualitative and quantitative constraints. We consider the means for solving key problems of reasoning over such logics: executability, augmentation, equivalence, and disjunctivity. As an algorithm for calculating the executability degree, we consider an extension of the tableau algorithm often used for first-order logic with solving simple numerical constraints. We prove that the algorithm is terminal, complete, and non-contradictory. We also provide several applications for the formal representation in natural language processing, including extending results of machine learning models, combining knowledge from multiple sources and formally describing uncertain facts.