@inproceedings{discovery10122601, pages = {168--182}, booktitle = {EPTCS 333 Proceedings of the 3rd Annual International Applied Category Theory Conference 2020}, editor = {D Spivak and J Vicary}, address = {Cambridge, MA, USA}, note = {This work is licensed under the Creative Commons Attribution License. http://creativecommons.org/licenses/by/3.0/}, publisher = {EPTCS}, year = {2021}, title = {Categorical vector space semantics for lambek calculus with a relevant modality (extended abstract)}, journal = {Electronic Proceedings in Theoretical Computer Science, EPTCS}, month = {February}, abstract = {We develop a categorical compositional distributional semantics for Lambek Calculus with a Relevant Modality, !L ? , 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 !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}, author = {McPheat, L and Sadrzadeh, M and Wazni, H and Wijnholds, G}, url = {https://cgi.cse.unsw.edu.au/~eptcs/content.cgi?ACT2020} }