Putting a Spin on Language: A Quantum Interpretation of Unary Connectives for Linguistic Applications

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