Quantum logic in dagger kernel categories

C. Heunen, B.P.F. Jacobs

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

3 Citations (Scopus)

Abstract

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.
Original languageEnglish
Title of host publicationProceedings of the 6th International Workshop on Quantum Logic Programming Languages (QPL 2009, Oxford, UK, April 8-9, 2009)
EditorsB. Coecke, P. Panangaden, P. Selinger
Pages79-103
DOIs
Publication statusPublished - 2011

Publication series

NameElectronic Notes in Theoretical Computer Science
Volume270(2)
ISSN (Print)1571-0061

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