Mathematical Foundations for a Compositional Distributional Model of Meaning

We propose a mathematical framework for a unification of the distributional
theory of meaning in terms of vector space models, and a compositional theory
for grammatical types, for which we rely on th ...

Towards Functorial Language-Games

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 space ...

An enriched category theory of language: from syntax to semantics

Given a piece of text, the ability to generate a coherent extension of it
implies some sophistication, including a knowledge of grammar and semantics. In
this paper, we propose a mathematical framewor ...

Grammar Equations

Diagrammatically speaking, grammatical calculi such as pregroups provide
wires between words in order to elucidate their interactions, and this enables
one to verify grammatical correctness of phrases ...

Towards Property-Based Tests in Natural Language

We consider a new approach to generate tests from natural language. Rather
than relying on machine learning or templated extraction from structured
comments, we propose to apply classic ideas from lin ...

Left Recursion in Parsing Expression Grammars

Parsing Expression Grammars (PEGs) are a formalism that can describe all
deterministic context-free languages through a set of rules that specify a
top-down parser for some language. PEGs are easy to ...

Autonomization of Monoidal Categories

We show that contrary to common belief in the DisCoCat community, a monoidal
category is all that is needed to define a categorical compositional model of
natural language. This relies on a constructi ...

Category-Theoretic Quantitative Compositional Distributional Models of Natural Language Semantics

This thesis is about the problem of compositionality in distributional
semantics. Distributional semantics presupposes that the meanings of words are
a function of their occurrences in textual context ...

Classical linear logic, cobordisms and categorial grammars

We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constit ...

On embedding Lambek calculus into commutative categorial grammars

Abstract categorial grammars (ACG), as well as some other, closely related systems, are based on the ordinary, commutative implicational linear logic and linear $\lambda$-calculus in contrast to the b ...