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Functorial Language Games for Question Answering

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 Publication date 2020
and research's language is English




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We present some categorical investigations into Wittgensteins language-games, with applications to game-theoretic pragmatics and question-answering in natural language processing.



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Distributional compositional (DisCo) models are functors that compute the meaning of a sentence from the meaning of its words. We show that DisCo models in the category of sets and relations correspond precisely to relational databases. As a consequence, we get complexity-theoretic reductions from semantics and entailment of a fragment of natural language to evaluation and containment of conjunctive queries, respectively. Finally, we define question answering as an NP-complete problem.
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In categorical compositional semantics of natural language one studies functors from a category of grammatical derivations (such as a Lambek pregroup) to a semantic category (such as real vector spaces). We compositionally build game-theoretic semantics of sentences by taking the semantic category to be the category whose morphisms are open games. This requires some modifications to the grammar category to compensate for the failure of open games to form a compact closed category. We illustrate the theory using simple examples of Wittgensteins language-games.
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Natural language understanding (NLU) of text is a fundamental challenge in AI, and it has received significant attention throughout the history of NLP research. This primary goal has been studied under different tasks, such as Question Answering (QA) and Textual Entailment (TE). In this thesis, we investigate the NLU problem through the QA task and focus on the aspects that make it a challenge for the current state-of-the-art technology. This thesis is organized into three main parts: In the first part, we explore multiple formalisms to improve existing machine comprehension systems. We propose a formulation for abductive reasoning in natural language and show its effectiveness, especially in domains with limited training data. Additionally, to help reasoning systems cope with irrelevant or redundant information, we create a supervised approach to learn and detect the essential terms in questions. In the second part, we propose two new challenge datasets. In particular, we create two datasets of natural language questions where (i) the first one requires reasoning over multiple sentences; (ii) the second one requires temporal common sense reasoning. We hope that the two proposed datasets will motivate the field to address more complex problems. In the final part, we present the first formal framework for multi-step reasoning algorithms, in the presence of a few important properties of language use, such as incompleteness, ambiguity, etc. We apply this framework to prove fundamental limitations for reasoning algorithms. These theoretical results provide extra intuition into the existing empirical evidence in the field.
147 - Yiwei Chen , Yu Pan , Daoyi Dong 2020
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