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

Abstract

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

arXiv commentIn Proceedings ACT 2020, arXiv:2101.07888. arXiv admin note: substantial text overlap with arXiv:2005.03074

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Cited by in corpus (3)

• Assessing the Unitary RNN as an End-to-End Compositional Model of Syntax
• DisCoCat for Donkey Sentences
• Categorical Vector Space Semantics for Lambek Calculus with a Relevant Modality