A Hyperintensional Theory of Intelligent Question Answering in TIL

Abstract

AbstractThe paper deals with natural language processing and question answering over large corpora of formalised natural language texts. Our background theory is the system of Transparent Intensional Logic (TIL) which is a partial, hyperintensional, typed \(\uplambda \)-calculus. Having a fine-grained analysis of natural language sentences in the form of TIL constructions, we apply Gentzen’s system of natural deduction adjusted for TIL to answer questions in an ‘intelligent’ way. It means that our system derives logical consequences entailed by the input sentences rather than merely searching answers by keywords. The theory of question answering must involve special rules rooted in the rich semantics of a natural language, and the TIL system makes it possible to formalise all the semantically salient features of natural languages in a fine-grained way. In particular, since TIL is a logic of partial functions, it is apt for dealing with non-referring terms and sentences with truth-value gaps. It is important because sentences often come attached with a presupposition that must be true so that a given sentence had any truth-value. And since answering is no less important than raising questions, we also propose a method of adequate unambiguous answering questions with presuppositions. In case the presupposition of a question is not true (because either false or ‘gappy’), there is no unambiguous direct answer, and an adequate complete answer is instead a negated presupposition. There are two novelties; one is the analysis and answering of Wh-questions that transform into \(\uplambda \)-terms referring to \(\upalpha \)-objects where \(\upalpha \) is not the type of a truth-value. The second is integration of special rules rooted in the semantics of natural language into Gentzen’s system of natural deduction, together with a heuristic method of searching relevant sentences in the labyrinth of input text data that is driven by constituents of a given question.KeywordsQuestion answeringWh-QuestionLambda calculusNatural deductionTransparent Intensional Logic TILAnaphoric referencesProperty modifiersFactive verbsPartialityPresuppositions