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

Lachlan McPheat
(University College London)
Mehrnoosh Sadrzadeh
(University College London)
Hadi Wazni
(Queen Mary University London)
Gijs Wijnholds
(Utrecht University)

We develop a categorical compositional distributional semantics for Lambek Calculus with a Relevant Modality, which has a limited version of the contraction and permutation rules. The categorical part of the semantics is a monoidal biclosed category with a coalgebra modality as defined on Differential Categories. 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 this extended calculus: 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

In David I. Spivak and Jamie Vicary: Proceedings of the 3rd Annual International Applied Category Theory Conference 2020 (ACT 2020), Cambridge, USA, 6-10th July 2020, Electronic Proceedings in Theoretical Computer Science 333, pp. 168–182.
Published: 8th February 2021.

ArXived at: http://dx.doi.org/10.4204/EPTCS.333.12 bibtex PDF

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