Reasoning about Meaning in Natural Language with Compact Closed Categories and Frobenius Algebras

Understand

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.