Related papers: Categorical Tools for Natural Language Processing
We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and…
Techniques in which words are represented as vectors have proved useful in many applications in computational linguistics, however there is currently no general semantic formalism for representing meaning in terms of vectors. We present a…
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…
Neural networks have become an increasingly popular tool for solving many real-world problems. They are a general framework for differentiable optimization which includes many other machine learning approaches as special cases. In this…
For building question answering systems and natural language interfaces, semantic parsing has emerged as an important and powerful paradigm. Semantic parsers map natural language into logical forms, the classic representation for many…
We describe a modular system for generating sentences from formal definitions of underlying linguistic structures using domain-specific languages. The system uses Java in general, Prolog for lexical entries and custom domain-specific…
Python is a popular high-level general-purpose programming language also heavily used by the scientific community. It supports a variety of different programming paradigms and is preferred by many for its ease of use. With the vision of…
Modelling compositionality has been a longstanding area of research in the field of vector space semantics. The categorical approach to compositionality maps grammar onto vector spaces in a principled way, but comes under fire for requiring…
With the increased interest in machine learning, and deep learning in particular, the use of automatic differentiation has become more wide-spread in computation. There have been two recent developments to provide the theoretical support…
This thesis deals with two main topics: virtual double categories as semantics environments for predicate logic, and a syntactic presentation of virtual double categories as a type theory. One significant principle of categorical logic is…
This paper addresses the problem of mapping natural language sentences to lambda-calculus encodings of their meaning. We describe a learning algorithm that takes as input a training set of sentences labeled with expressions in the lambda…
A new categorical framework is provided for dealing with multiple arguments in a programming language with effects, for example in a language with imperative features. Like related frameworks (Monads, Arrows, Freyd categories), we…
Techniques are presented for defining models of computational linguistics theories. The methods of generalized diagrams that were developed by this author for modeling artificial intelligence planning and reasoning are shown to be…
We show that three fixed point structures equipped with (sequential) composition, a sum operation, and a fixed point operation share the same valid equations. These are the theories of (context-free) languages, (regular) tree languages, and…
This document is an elementary introduction to string diagrams. It takes a computer science perspective: rather than using category theory as a starting point, we build on intuitions from formal language theory, treating string diagrams as…
The ability to compose parts to form a more complex whole, and to analyze a whole as a combination of elements, is desirable across disciplines. This workshop bring together researchers applying compositional approaches to physics, NLP,…
The Categorical Compositional Distributional (DisCoCat) framework models meaning in natural language using the mathematical framework of quantum theory, expressed as formal diagrams. DisCoCat diagrams can be associated with tensor networks…
A theory of data types based on category theory is presented. We organize data types under a new categorical notion of F,G-dialgebras which is an extension of the notion of adjunctions as well as that of T-algebras. T-algebras are also used…
Computer programs are often factored into pure components -- simple, total functions from inputs to outputs -- and components that may have side effects -- errors, changes to memory, parallel threads, abortion of the current loop, etc. We…
This article serves as a preliminary introduction to the design of a new, open-source applied and computational category theory framework, named Categorica, built on top of the Wolfram Language. Categorica allows one to configure and…