Reasoning about meaning in natural language with compact closed categories and Frobenius algebras

Abstract

Compact closed categories have found applications in modeling quantum information protocols by Abramsky-Coecke. They also provide semantics for Lambek's pregroup algebras, applied to formalizing the grammatical structure of natural language, and are implicit in a distributional model of word meaning based on vector spaces. Specifically, in previous work Coecke-Clark-Sadrzadeh used the product category of pregroups with vector spaces and provided a distributional model of meaning for sentences. We recast this theory in terms of strongly monoidal functors and advance it via Frobenius algebras over vector spaces. The former are used to formalize topological quantum field theories by Atiyah and Baez-Dolan, and the latter are used to model classical data in quantum protocols by Coecke-Pavlovic-Vicary. The Frobenius algebras enable us to work in a single space in which meanings of words, phrases, and sentences of any structure live. Hence we can compare meanings of different language constructs and enhance the applicability of the theory. We report on experimental results on a number of language tasks and verify the theoretical predictions. *

Engineering General Intelligence, Part 2

“…The use of a pair of word classes to define a link type is a basic premise of categorial grammar [KSPC13]. The use of a pair of word classes to define a link type is a basic premise of categorial grammar [KSPC13].…”

“…An introduction to type theory can be found in [Pro13], and an application of type theory to linguistics can be found in [KSPC13]. An introduction to type theory can be found in [Pro13], and an application of type theory to linguistics can be found in [KSPC13].…”

Natural language semantics in biproduct dagger categories

“…This means that the compositional semantics of [Kartsaklis et al, 2013] can be generalised to an arbitrary semantic category.…”

“…The compositional semantics of [Clark et al, 2008] and [Kartsaklis et al, 2013] for vector space models in FdVect R also use pregroup grammars and a 'functorial method'. This claim has to be taken with a caveat.…”

From Natural Language to RDF Graphs with Pregroups

“…They include the compositional distributional vector space models of (Clark et al, 2008), (Kartsaklis et al, 2013) based on context and the functional logical models of (Preller, 2012).…”