Vector Space Semantics for Lambek Calculus with Soft Subexponentials
This work addresses the need for a decidable and linear theory in computational linguistics for modeling complex linguistic phenomena, offering a foundational improvement over previous nonlinear approaches.
The paper tackles the problem of providing a vector space semantics for Lambek Calculus with Soft Subexponentials, enabling compositional vector interpretations for complex linguistic structures like parasitic gaps and discourse units, and demonstrates its application in a distributional sentence similarity task with experimental results.
We develop a vector space semantics for Lambek Calculus with Soft Subexponentials, apply the calculus to construct compositional vector interpretations for parasitic gap noun phrases and discourse units with anaphora and ellipsis, and experiment with the constructions in a distributional sentence similarity task. As opposed to previous work, which used Lambek Calculus with a Relevant Modality the calculus used in this paper uses a bounded version of the modality and is decidable. The vector space semantics of this new modality allows us to meaningfully define contraction as projection and provide a linear theory behind what we could previously only achieve via nonlinear maps.