DisCoCat (Categorical Compositional Distributional) is a mathematical framework for natural language processing which uses category theory to unify distributional semantics with the principle of compositionality.
The grammatical derivations in a categorial grammar (usually a pregroup grammar) are interpreted as linear maps acting on the tensor product of word vectors to produce the meaning of a sentence or a piece of text.
String diagrams are used to visualise information flow and reason about natural language semantics.
The framework was first introduced by Bob Coecke, Mehrnoosh Sadrzadeh, and Stephen Clark[1] as an application of categorical quantum mechanics to natural language processing.
It started with the observation that pregroup grammars and quantum processes shared a common mathematical structure: they both form a rigid category (also known as a non-symmetric compact closed category).
As such, they both benefit from a graphical calculus, which allows a purely diagrammatic reasoning.
[2][3][4] There are multiple definitions of DisCoCat in the literature, depending on the choice made for the compositional aspect of the model.
The common denominator between all the existent versions, however, always involves a categorical definition of DisCoCat as a structure-preserving functor from a category of grammar to a category of semantics, which usually encodes the distributional hypothesis.
The original paper[1] used the categorical product of FinVect with a pregroup seen as a posetal category.
This approach has some shortcomings: all parallel arrows of a posetal category are equal, which means that pregroups cannot distinguish between different grammatical derivations for the same syntactically ambiguous sentence.
[5] A more intuitive manner of saying the same is that one works with diagrams rather than with partial orders when describing grammar.
This problem is overcome when one considers the free rigid category
which can be represented as string diagrams with cups and caps, i.e. adjunction units and counits.
[7] With this definition of pregroup grammars as free rigid categories, DisCoCat models can be defined as strong monoidal functors
Spelling things out in detail, they assign a finite dimensional vector space
in the appropriate tensor product space to each dictionary entry
as the category of semantics is that vector spaces are the usual setting of distributional reading in computational linguistics and natural language processing.
The underlying idea of distributional hypothesis "A word is characterized by the company it keeps" is particularly relevant when assigning meaning to words like adjectives or verbs, whose semantic connotation is strongly dependent on context.
Variations of DisCoCat have been proposed with a different choice for the grammar category.
The DisCoCat framework has been used to study the following phenomena from linguistics.
The DisCoCat framework has been applied to solve the following tasks in natural language processing.