The Frobenius anatomy of word meanings II: possessive relative pronouns*

40 pages, Journal of Logic and Computation, Essays dedicated to Roy Dyckhoff on the occasion of his retirement, S. Graham-Lengrand and D. Galmiche (eds.), 201

A Corpus-based Toy Model for DisCoCat

The categorical compositional distributional (DisCoCat) model of meaning rigorously connects distributional semantics and pregroup grammars, and has found a variety of applications in computational linguistics. From a more abstract standpoint, the DisCoCat paradigm predicates the construction of a mapping from syntax to categorical semantics. In this work we present a concrete construction of one such mapping, from a toy model of syntax for corpora annotated with constituent structure trees, to categorical semantics taking place in a category of free R-semimodules over an involutive commutative semiring R.Comment: In Proceedings SLPCS 2016, arXiv:1608.0101

A Frobenius Algebraic Analysis for Parasitic Gaps

The interpretation of parasitic gaps is an ostensible case of non-linearity in natural language composition. Existing categorial analyses, both in the typelogical and in the combinatory traditions, rely on explicit forms of syntactic copying. We identify two types of parasitic gapping where the duplication of semantic content can be confined to the lexicon. Parasitic gaps in adjuncts are analysed as forms of generalized coordination with a polymorphic type schema for the head of the adjunct phrase. For parasitic gaps affecting arguments of the same predicate, the polymorphism is associated with the lexical item that introduces the primary gap. Our analysis is formulated in terms of Lambek calculus extended with structural control modalities. A compositional translation relates syntactic types and derivations to the interpreting compact closed category of finite dimensional vector spaces and linear maps with Frobenius algebras over it. When interpreted over the necessary semantic spaces, the Frobenius algebras provide the tools to model the proposed instances of lexical polymorphism.Comment: SemSpace 2019, to appear in Journal of Applied Logic

A Study of Entanglement in a Categorical Framework of Natural Language

In both quantum mechanics and corpus linguistics based on vector spaces, the notion of entanglement provides a means for the various subsystems to communicate with each other. In this paper we examine a number of implementations of the categorical framework of Coecke, Sadrzadeh and Clark (2010) for natural language, from an entanglement perspective. Specifically, our goal is to better understand in what way the level of entanglement of the relational tensors (or the lack of it) affects the compositional structures in practical situations. Our findings reveal that a number of proposals for verb construction lead to almost separable tensors, a fact that considerably simplifies the interactions between the words. We examine the ramifications of this fact, and we show that the use of Frobenius algebras mitigates the potential problems to a great extent. Finally, we briefly examine a machine learning method that creates verb tensors exhibiting a sufficient level of entanglement.Comment: In Proceedings QPL 2014, arXiv:1412.810

A Generalised Quantifier Theory of Natural Language in Categorical Compositional Distributional Semantics with Bialgebras

Categorical compositional distributional semantics is a model of natural language; it combines the statistical vector space models of words with the compositional models of grammar. We formalise in this model the generalised quantifier theory of natural language, due to Barwise and Cooper. The underlying setting is a compact closed category with bialgebras. We start from a generative grammar formalisation and develop an abstract categorical compositional semantics for it, then instantiate the abstract setting to sets and relations and to finite dimensional vector spaces and linear maps. We prove the equivalence of the relational instantiation to the truth theoretic semantics of generalised quantifiers. The vector space instantiation formalises the statistical usages of words and enables us to, for the first time, reason about quantified phrases and sentences compositionally in distributional semantics