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      A Typedriven Vector Semantics for Ellipsis with Anaphora using Lambek Calculus with Limited Contraction

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          Abstract

          We develop a vector space semantics for verb phrase ellipsis with anaphora using type-driven compositional distributional semantics based on the Lambek calculus with limited contraction (LCC) of J\"ager (2006). Distributional semantics has a lot to say about the statistical collocation-based meanings of content words, but provides little guidance on how to treat function words. Formal semantics on the other hand, has powerful mechanisms for dealing with relative pronouns, coordinators, and the like. Type-driven compositional distributional semantics brings these two models together. We review previous compositional distributional models of relative pronouns, coordination and a restricted account of ellipsis in the DisCoCat framework of Coecke et al. (2010, 2013). We show how DisCoCat cannot deal with general forms of ellipsis, which rely on copying of information, and develop a novel way of connecting typelogical grammar to distributional semantics by assigning vector interpretable lambda terms to derivations of LCC in the style of Muskens & Sadrzadeh (2016). What follows is an account of (verb phrase) ellipsis in which word meanings can be copied: the meaning of a sentence is now a program with non-linear access to individual word embeddings. We present the theoretical setting, work out examples, and demonstrate our results on a toy distributional model motivated by data.

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          Composition in distributional models of semantics.

          Vector-based models of word meaning have become increasingly popular in cognitive science. The appeal of these models lies in their ability to represent meaning simply by using distributional information under the assumption that words occurring within similar contexts are semantically similar. Despite their widespread use, vector-based models are typically directed at representing words in isolation, and methods for constructing representations for phrases or sentences have received little attention in the literature. This is in marked contrast to experimental evidence (e.g., in sentential priming) suggesting that semantic similarity is more complex than simply a relation between isolated words. This article proposes a framework for representing the meaning of word combinations in vector space. Central to our approach is vector composition, which we operationalize in terms of additive and multiplicative functions. Under this framework, we introduce a wide range of composition models that we evaluate empirically on a phrase similarity task.
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            Computational interpretations of linear logic

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              Type Grammar Revisited

              J. Lambek (1999)
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                Author and article information

                Journal
                05 May 2019
                Article
                1905.01647
                f9371cb1-d593-4467-bd0e-399511618114

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                Forthcoming in: Journal of Logic, Language and Information
                cs.CL cs.AI cs.LO math.LO

                Theoretical computer science,Artificial intelligence,Logic & Foundation
                Theoretical computer science, Artificial intelligence, Logic & Foundation

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