Categorical Vector Space Semantics for Lambek Calculus with a Relevant Modality (Extended 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 tensorsComment: In Proceedings ACT 2020, arXiv:2101.07888. arXiv admin note: substantial text overlap with arXiv:2005.0307

Categorical Vector Space Semantics for Lambek Calculus with a Relevant Modality

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

Parsing logical grammar: CatLog3

CatLog3 is a Prolog parser/theorem-prover for (type) logical (categorial) grammar. In such logical grammar, grammar is reduced to logic: a string of words is grammatical if and only if an associated logical statement is a theorem. CalLog3 implements a logic extending displacement calculus, a sublinear fragment including as primitive connectives the continuous (Lambek) and discontinuous wrapping connectives of the displacement calculus, additives, 1st order quantifiers, normal modalities, bracket modalities and subexponentials. In this paper we survey how CatLog3 is implemented on the principles of Andreoli’s focusing and a generalisation of van Benthem’s count-invariance.Peer ReviewedPostprint (published version

Grammar logicised: relativisation

Many variants of categorial grammar assume an underlying logic which is associative and linear. In relation to left extraction, the former property is challenged by island domains, which involve nonassociativity, and the latter property is challenged by parasitic gaps, which involve nonlinearity. We present a version of type logical grammar including ‘structural inhibition’ for nonassociativity and ‘structural facilitation’ for nonlinearity and we give an account of relativisation including islands and parasitic gaps and their interaction.Peer ReviewedPostprint (published version