Grammátrix

Grammátrix is a theoretical construct used in linguistics to represent grammatical rules and relationships in matrix form. It encodes how features across words combine to produce grammatical structures, facilitating compact representation and algebraic manipulation. Grammátrix is not tied to any single theory, and can be instantiated within various frameworks such as phrase structure, dependency grammar, or feature-based approaches.

In a Grammátrix, each dimension corresponds to a grammatical feature or syntactic relation (such as number, case, tense, agreement, or subject–verb relation). Entries indicate allowable combinations or transitions between features. Sentences can be modeled by applying matrix operations to feature vectors or by composing matrices for successive constituents.

Applications include computational parsing, language modeling, and psycholinguistic simulations. Grammátrix can help constrain possible parses, propagate features across constituents, and represent optional elements as flexible entries that permit alternative paths.

The term Grammátrix appears in some theoretical discussions and is not universally adopted. Variants differ in mapping rules to matrix entries; data sparsity and interpretability are common concerns for practitioners.

See also: grammar matrix, dependency grammar, feature structures, formal grammar, matrix algebra in linguistics.