Reprezentace komputačních znalostí a návrh inferenčního stroje pro TIL

Abstract

This work deals with the design of an inference machine for natural-language processing in general, and in particular, with deductive reasoning over the base of textual data. In order to be able to derive implicit or computable knowledge from explicit knowledge recorded in the texts, it is necessary to apply logical deductive methods. Our background system applicable to the analysis of natural language sentences is Transparent Intensional Logic (TIL). From the formal point of view, TIL is a hyperintensional, partial typed lambda calculus with procedural semantics. For the purpose of inferences, it is necessary to define a sound proof calculus that would reflect all the technical aspects of TIL as well as the rules rooted in the rich semantics of natural languages. The resulting calculus can serve as the specification of the inferential machine that would control the process of automatic proving by extracting relevant rules and constructions to which the inference rules are applied. In this work, we focus on the theoretical aspects of the inference machine, i.e. the specification of the sound proof calculus for TIL. The main novelty of this work is the specification of two proof calculi. They are the system of natural deduction and the general resolution method, both adjusted for the needs of applications in TIL and natural language processing. The second novelty is the comparison of advantages and disadvantages of these systems. The adjustments concern technical features of TIL as a hyperintesional logic of partial functions. In addition, the calculus must be enriched by the semantic rules of a natural language. Another novelty of this work is the proof of the validity of Church-Rossser theorem and Henkin completeness of the Hyperintensional Typed Lambda Calculus (HTLC) system. The HTLC system has been inspired by TIL. It can be characterized as a modification of a syntactically defined version of the typed lambda calculus of total functions enriched with the hyperintensional terms denoting constructions.