Putting a Spin on Language: A Quantum Interpretation of Unary Connectives for Linguistic Applications
This work addresses a specific issue in computational linguistics for modeling linguistic ambiguity, but it is incremental as it builds on existing directional density matrix semantics.
The paper tackles the problem of representing derivational ambiguities in extended Lambek Calculus for computational linguistics by turning control modalities into first-class citizens in vectorial interpretation, resulting in a method that simultaneously represents co-existing interpretations of ambiguous utterances using orthogonal spin states.
Extended versions of the Lambek Calculus currently used in computational linguistics rely on unary modalities to allow for the controlled application of structural rules affecting word order and phrase structure. These controlled structural operations give rise to derivational ambiguities that are missed by the original Lambek Calculus or its pregroup simplification. Proposals for compositional interpretation of extended Lambek Calculus in the compact closed category of FVect and linear maps have been made, but in these proposals the syntax-semantics mapping ignores the control modalities, effectively restricting their role to the syntax. Our aim is to turn the modalities into first-class citizens of the vectorial interpretation. Building on the directional density matrix semantics, we extend the interpretation of the type system with an extra spin density matrix space. The interpretation of proofs then results in ambiguous derivations being tensored with orthogonal spin states. Our method introduces a way of simultaneously representing co-existing interpretations of ambiguous utterances, and provides a uniform framework for the integration of lexical and derivational ambiguity.