Categorical Vector Space Semantics for Lambek Calculus with a Relevant Modality

• URL: http://arxiv.org/abs/2005.03074v4
• Date: Thu, 11 May 2023 14:55:08 GMT
• Title: Categorical Vector Space Semantics for Lambek Calculus with a Relevant Modality
• Authors: Lachlan McPheat, Mehrnoosh Sadrzadeh, Hadi Wazni, Gijs Wijnholds
• Abstract summary: We develop a categorical distributional semantics for Lambek Calculus with a Relevantity!L*. We instantiate this category to finite dimensional vector spaces and linear maps via "quantisation" functors. 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.
• Score: 3.345437353879255
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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