Mcpheat, L; Wijnholds, G; Sadrzadeh, M; Correia, A; Toumi, A; (2021) Anaphora and Ellipsis in Lambek Calculus with a Relevant Modality: Syntax and Semantics. Journal of Cognitive Science , 22 (2) pp. 1-34.

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Abstract

Lambek calculus with a relevant modality !L* of (Kanovich et al., 2016) syntactically resolves parasitic gaps in natural language. It resembles the Lambek calculus with anaphora LA of (Jäger, 1998) and the Lambek calculus with controlled contraction L(Formula presented) of (Wijnholds and Sadrzadeh, 2019b) which deal with anaphora and ellipsis. What all these calculi add to Lambek calculus is a copying and moving behaviour. Distributional semantics is a subfield of Natural Language Processing that uses vector space semantics for words via co-occurrence statistics in large corpora of data. Compositional vector space semantics for Lambek Calculi are obtained via the DisCoCat models (Coecke et al., 2010). LA does not have a vector space semantics and the semantics of L(Formula presented) is not compositional. Previously, we developed a DisCoCat semantics for !L* and focused on the parasitic gap applications. In this paper, we use the vector space instance of that general semantics and show how one can also interpret anaphora, ellipsis, and for the first time derive the sloppy vs strict vector readings of ambiguous anaphora with ellipsis cases. The base of our semantics is tensor algebras and their finite dimensional variants: the Fermionic Fock spaces of Quantum Mechanics. We implement our model and experiment with the ellipsis disambiguation task of (Wijnholds and Sadrzadeh, 2019a).

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