Building a shared world: mapping distributional to model-theoretic semantic spaces

Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing, pages 22–32, Lisbon, Portugal, 17-21 September 2015. c⃝2015 Association for Computational Linguistics. Building a shared world: Mapping distributional to model-theoretic semantic spaces Aur´elie Herbelot Universit¨at Stuttgart Institut f¨ur Maschinelle Sprachverarbeitung Stuttgart, Germany aurelie.herbelot@cantab.net Eva Maria Vecchi University of Cambridge Computer Laboratory Cambridge, UK eva.vecchi@cl.cam.ac.uk Abstract In this paper, we introduce an approach to au- tomatically map a standard distributional se- mantic space onto a set-theoretic model. We predict that there is a functional relationship between distributional information and vecto- rial concept representations in which dimen- sions are predicates and weights are gener- alised quantifiers. In order to test our pre- diction, we learn a model of such relation- ship over a publicly available dataset of feature norms annotated with natural language quan- tifiers. Our initial experimental results show that, at least for domain-specific data, we can indeed map between formalisms, and generate high-quality vector representations which en- capsulate set overlap information. We further investigate the generation of natural language quantifiers from such vectors. 1 Introduction In recent years, the complementarity of distributional and formal semantics has become increasingly evi- dent. While distributional semantics (Turney and Pan- tel, 2010; Clark, 2012; Erk, 2012) has proved very suc- cessful in modelling lexical effects such as graded sim- ilarity and polysemy, it clearly has difficulties account- ing for logical phenomena which are well covered by model-theoretic semantics (Grefenstette, 2013). A number of proposals have emerged from these considerations, suggesting that an overarching seman- tics integrating both distributional and formal aspects would be desirable (Coecke et al., 2011; Bernardi et al., 2013; Grefenstette, 2013; Baroni et al., 2014a; Garrette et al., 2013; Beltagy et al., 2013; Lewis and Steedman, 2013). We will use the term ‘Formal Distributional Se- mantics’ (FDS) to refer to such proposals. This paper follows this line of work, focusing on one central ques- tion: the formalisation of the systematic dependencies between lexical and set-theoretic levels. Let us consider the following examples. 1. Kim writes books. 2. Kim likes books. The preferred reading of 1 has a logical form where the object is treated as an existential, while the object in 2 has a generic reading: • ∃x∗[book′(x∗) ∧ write′(Kim, x∗)] • GEN x[book′(x) → like′(Kim, x)] with x∗ indicating a plurality and GEN the generic quantifier. It is generally accepted that the appropriate choice of quantifier for an ambiguous bare plural object de- pends, amongst other things, on the lexical semantics of the verb (e.g. Glasbey (2006)). This type of inter- action implies the existence of systematic influences of the lexicon over logic, which could in principle be for- malised. A model of the lexicon/logic interface would be de- sirable to explain how speakers resolve standard cases of ambiguity like the bare plural in 1 and 2, but more generally, it could be the basis for answering a more fundamental question: how do speakers construct a model of a sentence for which they have no prior per- ceptual …

Content truncated to 500 words