Categorical Vector Space Semantics for Lambek Calculus with a Relevant Modality (Extended Abstract)

We develop a categorical compositional distributional semantics for Lambek Calculus with Relevant Modality, which has limited version of the contraction and permutation rules. The part is monoidal biclosed category coalgebra modality as defined on Differential Categories. instantiate this to finite dimensional vector spaces linear maps via quantisation functors work three concrete interpretations modality. apply model construct semantic motivating example extended calculus: derivation phrase parasitic gap. effectiveness are evaluated disambiguation task, an extension sentence dataset gap phrases, using BERT, Word2Vec, FastText vectors Relational tensors