eprintid: 10122601 rev_number: 19 eprint_status: archive userid: 608 dir: disk0/10/12/26/01 datestamp: 2021-03-09 10:05:44 lastmod: 2021-10-15 22:33:31 status_changed: 2021-03-09 10:05:44 type: proceedings_section metadata_visibility: show creators_name: McPheat, L creators_name: Sadrzadeh, M creators_name: Wazni, H creators_name: Wijnholds, G title: Categorical vector space semantics for lambek calculus with a relevant modality (extended abstract) ispublished: pub divisions: UCL divisions: B04 divisions: C05 divisions: F48 note: This work is licensed under the Creative Commons Attribution License. http://creativecommons.org/licenses/by/3.0/ 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 date: 2021-02-08 publisher: EPTCS official_url: https://cgi.cse.unsw.edu.au/~eptcs/content.cgi?ACT2020 oa_status: green full_text_type: pub language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 1845688 doi: 10.4204/eptcs.333.12 lyricists_name: Sadrzadeh, Mehrnoosh lyricists_id: MSADR73 actors_name: Bracey, Alan actors_id: ABBRA90 actors_role: owner full_text_status: public publication: Electronic Proceedings in Theoretical Computer Science, EPTCS place_of_pub: Cambridge, MA, USA pagerange: 168-182 event_title: 3rd Annual International Applied Category Theory Conference 2020 book_title: EPTCS 333 Proceedings of the 3rd Annual International Applied Category Theory Conference 2020 editors_name: Spivak, D editors_name: Vicary, J citation: McPheat, L; Sadrzadeh, M; Wazni, H; Wijnholds, G; (2021) Categorical vector space semantics for lambek calculus with a relevant modality (extended abstract). In: Spivak, D and Vicary, J, (eds.) EPTCS 333 Proceedings of the 3rd Annual International Applied Category Theory Conference 2020. (pp. pp. 168-182). EPTCS: Cambridge, MA, USA. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10122601/1/2101.10486v1.pdf