Categorical Vector Space Semantics for Lambek Calculus with a Relevant Modality
This provides a formal semantic framework for computational linguistics, specifically addressing parasitic gap constructions, but appears incremental relative to existing categorical semantics approaches.
The authors developed a categorical compositional distributional semantics for Lambek Calculus with a Relevant Modality (!L*) to model linguistic phenomena like parasitic gaps, and evaluated it on a disambiguation task using word embeddings like BERT and Word2Vec.
We develop a categorical compositional distributional semantics for Lambek Calculus with a Relevant Modality !L*, which has a limited edition of the contraction and permutation rules. The categorical part of the semantics is a monoidal biclosed category with a coalgebra modality, very similar to the structure of a Differential Category. We instantiate this category to finite dimensional vector spaces and linear maps via "quantisation" functors and work with three concrete interpretations of the coalgebra modality. We apply the model to construct categorical and concrete semantic interpretations for the motivating example of !L*: the derivation of a phrase with a parasitic gap. The effectiveness of the concrete interpretations are evaluated via a disambiguation task, on an extension of a sentence disambiguation dataset to parasitic gap phrases, using BERT, Word2Vec, and FastText vectors and Relational tensors.