Related papers: Categorial Minimalist Grammar
Analyzing relational languages by their logical expressiveness is well understood. Something not well understood or even formalized is the vague concept of relational query patterns. What are query patterns? And how can we reason about…
Evans and Gazdar introduced DATR as a simple, non-monotonic language for representing natural language lexicons. Although a number of implementations of DATR exist, the full language has until now lacked an explicit, declarative semantics.…
This thesis develops the translation between category theory and computational linguistics as a foundation for natural language processing. The three chapters deal with syntax, semantics and pragmatics. First, string diagrams provide a…
Recent research in computational linguistics has developed algorithms which associate matrices with adjectives and verbs, based on the distribution of words in a corpus of text. These matrices are linear operators on a vector space of…
The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain…
We give an exposition of the semantics of the simply-typed lambda-calculus, and its linear and ordered variants, using multi-ary structures. We define universal properties for multicategories, and use these to derive familiar rules for…
The major concern in the study of categories of logics is to describe condition for preservation, under the a method of combination of logics, of meta-logical properties. Our complementary approach to this field is study the "global"…
We develop a categorical compositional distributional semantics for Lambek Calculus with a Relevant Modality !L*, which has a limited edition of the contraction and permutation rules. The categorical part of the semantics is a monoidal…
We provide a Lawvere-style definition for partial theories, extending the classical notion of equational theory by allowing partially defined operations. As in the classical case, our definition is syntactic: we use an appropriate class of…
Abstract grammatical knowledge - of parts of speech and grammatical patterns - is key to the capacity for linguistic generalization in humans. But how abstract is grammatical knowledge in large language models? In the human literature,…
Large Language Models (LLMs) excel at linear reasoning tasks but remain underexplored on non-linear structures such as those found in natural debates, which are best expressed as argument graphs. We evaluate whether LLMs can approximate…
With a view towards models of quantum computation and/or the interpretation of linear logic, we define a functional language where all functions are linear operators by construction. A small step operational semantic (and hence an…
This paper presents a model for linguistic description based on group theory. A grammar in this model, or "G-grammar", is a collection of lexical expressions which are products of logical forms, phonological forms, and their inverses.…
There is a growing need for abstractions in logic specification languages such as FO(.) and ASP. One technique to achieve these abstractions are templates (sometimes called macros). While the semantics of templates are virtually always…
In a recent paper, a realizability technique has been used to give a semantics of a quantum lambda calculus. Such a technique gives rise to an infinite number of valid typing rules, without giving preference to any subset of those. In this…
Neural language models (LMs) perform well on tasks that require sensitivity to syntactic structure. Drawing on the syntactic priming paradigm from psycholinguistics, we propose a novel technique to analyze the representations that enable…
One of the fundamental requirements for models of semantic processing in dialogue is incrementality: a model must reflect how people interpret and generate language at least on a word-by-word basis, and handle phenomena such as fragments,…
Compositional knowledge representations in reinforcement learning (RL) facilitate modular, interpretable, and safe task specifications. However, generating compositional models requires the characterization of minimal assumptions for the…
The AMR (Abstract Meaning Representation) formalism for representing meaning of natural language sentences was not designed to deal with scope and quantifiers. By extending AMR with indices for contexts and formulating constraints on these…
In this work we define formal grammars in terms of free monoidal categories, along with a functor from the category of formal grammars to the category of automata. Generalising from the Booleans to arbitrary semirings, we extend our…