TY - GEN

T1 - Quantum logic in dagger kernel categories

AU - Heunen, C.

AU - Jacobs, B.P.F.

PY - 2011

Y1 - 2011

N2 - This paper investigates quantum logic from the perspective of categorical logic, and starts from minimal assumptions, namely the existence of involutions/daggers and kernels. The resulting structures turn out to (1) encompass many examples of interest, such as categories of relations, partial injections, Hilbert spaces (also modulo phase), and Boolean algebras, and (2) have interesting categorical/logical properties, in terms of kernel fibrations, such as existence of pullbacks, factorisation, and orthomodularity. For instance, the Sasaki hook and and-then connectives are obtained, as adjoints, via the existential-pullback adjunction between fibres.

AB - This paper investigates quantum logic from the perspective of categorical logic, and starts from minimal assumptions, namely the existence of involutions/daggers and kernels. The resulting structures turn out to (1) encompass many examples of interest, such as categories of relations, partial injections, Hilbert spaces (also modulo phase), and Boolean algebras, and (2) have interesting categorical/logical properties, in terms of kernel fibrations, such as existence of pullbacks, factorisation, and orthomodularity. For instance, the Sasaki hook and and-then connectives are obtained, as adjoints, via the existential-pullback adjunction between fibres.

U2 - 10.1016/j.entcs.2011.01.024

DO - 10.1016/j.entcs.2011.01.024

M3 - Conference contribution

T3 - Electronic Notes in Theoretical Computer Science

SP - 79

EP - 103

BT - Proceedings of the 6th International Workshop on Quantum Logic Programming Languages (QPL 2009, Oxford, UK, April 8-9, 2009)

A2 - Coecke, B.

A2 - Panangaden, P.

A2 - Selinger, P.

ER -