Categorical Vector Space Semantics for Lambek Calculus with a Relevant Modality

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 phrase one, using BERT, Word2Vec, and FastText vectors and Relational tensors.

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

“…The above Cogebra construction can be simplified when one works with free vector spaces, for details of which we refer to the full version of the paper [25]. The simplified version resembles half of a bialgebra over FdVect R , known as Special Frobenius bialgebras, which were used in [36,28,26] to model relative pronouns in English and Dutch.…”

“…The !L * derivation of "the paper that John signed without reading" is in the full version of the paper [25]. The categorical semantics of this derivation is the following linear map.…”

“…The diagrammatic interpretation of the !L * -derivation is depicted in figure 2 This is obtained via steps mirroring the steps of the derivation tree of the example, please see the full version of the paper [25].…”

“…We experimented with three neural embedding architectures: BERT [10], FastText (FT) [6], and Word2Vec CBOW (W2V) [40]. For details of the training, please see the full version of the paper [25].…”

“…The experiment is performed using different neural word embeddings and on a disambiguation task over an extended version of dataset of [16] from transitive sentences to phrases with parasitic gaps. This paper is an extended abstract of the full arXiv paper [25].…”