The goal of this paper is to introduce the design of a question-answering system that makes it possible to retrieve answers to questions like “Is Tom a student?”, or “Who is the Miss World 2019?” from the large corpora of natural language texts. These texts are formalized automatically into the form of TIL constructions encoded in the TIL-Script language. TIL-Script is a computational variant of Pavel Tichý’s Transparent Intensional Logic (TIL). TIL is a hyperintensional, typed lambda calculus of partial functions. Hyperintensional, because the TIL terms are interpreted as denoting procedures rather than their products, which are partial functions-in-extension. These procedures are rigorously defined as TIL constructions. Since TIL is a logic of partial functions, in particular propositions with a truth-value gap, it is apt for dealing with questions that come attached with presuppositions. If a presupposition of a question is not true, there is no direct answer to such a question. We introduce basic classification of questions and answers, propose their TIL analysis and the way of evaluation, which then serve as a specification for implementation of the system.