A New Connective in Natural Deduction, and its Application to Quantum Computing

We investigate an unsuspected connection between non harmonious logical connectives, such as Prior's tonk, and quantum computing. We defend the idea that non harmonious connectives model the information erasure, the non-reversibility, and the non-determinism that occur, among other places, in quantum measurement. More concretely, we introduce a propositional logic with a non harmonious connective sup, prove cut elimination for this logic, and show that its proof language forms the core of a quantum programming language.