@unpublished(AbrBrand:UnifiedSTANLC, author = "Samson Abramsky and Adam Brandenburger", year = "2011", title = "A Unified Sheaf-Theoretic Account of Non-Locality and Contextuality", note = "ArXiv:quant-ph/1102.0264v2", ) @article(BanMulv:GlobalisationGDT, author = "Bernhard Banaschewski and Christopher J. Mulvey", year = "2006", title = "A Globalisation of the {G}elfand Duality Theorem", journal = "Annals of Pure and Applied Logic", volume = "137", pages = "62--103", doi = "10.1016/j.apal.2005.05.018", ) @article(CaspersHLS:IntQLnLS, author = "Martijn Caspers and Chris Heunen and Nicolaas P. Landsman and Bas Spitters", year = "2009", title = "Intuitionistic Quantum Logic of an $n$-level System", journal = "Foundations of Physics", volume = "39", pages = "731--759", doi = "10.1007/s10701-009-9308-7", ) @article(CoqSpit:IntVal, author = "Thierry Coquand and Bas Spitters", year = "2009", title = "{Integrals and Valuations}", journal = "Journal of Logic and Analysis", volume = "1", number = "3", pages = "1--22", doi = "10.4115/jla.2009.1.3", ) @article(Doering:QuStMSP, author = "Andreas D\"{o}ring", year = "2009", title = "Quantum States and Measures on the Spectral Presheaf", journal = "Advanced Science Letters", volume = "2", number = "2", pages = "291--301", ) @unpublished(DoeringIsham:ClassicalQPTV, author = "Andreas D\"{o}ring and Chris Isham", year = "2011", title = "Classical and Quantum Probabilities as Truth Values", note = "ArXiv:1102.2213", ) @incollection(DoeringIsham:WhatThingTTFP, author = "Andreas D\"{o}ring and Chris Isham", year = "2011", title = "`{W}hat is a {T}hing?': Topos Theory in the Foundations of Physics", editor = "Bob Coecke", booktitle = "{New Structures for Physics}", chapter = "13", series = "Lecture Notes in Physics", volume = "813", publisher = "Springer Verlag", address = "Berlin Heidelberg", pages = "753--937", doi = "10.1007/978-3-642-12821-9\_13", note = "ArXiv:0803.0417v1.", ) @inproceedings(FourmanScott:SheavesLogic, author = "M.P. Fourman and D.S. Scott", year = "1979", title = "Sheaves and Logic", editor = "M.P. Fourman and C.J. Mulvey and D.S. Scott", booktitle = "Applications of Sheaves", series = "Lecture Notes in Mathematics", volume = "753", publisher = "Springer-Verlag", pages = "302--401", doi = "10.1007/BFb0061824", ) @incollection(Giry:CatProb, author = "M. Giry", year = "1981", title = "A Categorical Approach to Probability Theory", booktitle = "Categorical Aspects of Topology and Analysis", series = "Lecture Notes in Mathematics", volume = "915", publisher = "Springer-Verlag", address = "Berlin", pages = "68--85", doi = "10.1007/s11225-010-9232-z", ) @inproceedings(Heckmann:ProbPDISL, author = "Reinhold Heckmann", year = "1994", title = "Probabilistic Power Domains, Information Systems, and Locales", editor = "Stephen Brookes and Michael Main and Austin Melton and David Schmidt", booktitle = "Mathematical Foundations in Programming Semantics -- 9th International Conference, 1993", series = "Lecture Notes in Computer Science", volume = "802", publisher = "Springer", address = "Berlin / Heidelberg", pages = "410--437", ) @inproceedings(HeunenLandsmanSpitters:Tovariance, author = "Chris Heunen and Nicolaas P. Landsman and Bas Spitters", year = "2008", title = "The Principle of General Tovariance", editor = "Rui Loja Fernandez and Roger Picken", booktitle = "Geometry and Physics, {X}{V}{I} {I}nternational {F}all {W}orkshop, {L}isbon, Portugal, 5-8 September 2007", series = "AIP Conference Proceedings, Mathematical and Statistical Physics", volume = "1023", publisher = "Springer", ) @article(HeunenLandsmanSpitters:ToposAQT, author = "Chris Heunen and Nicolaas P. Landsman and Bas Spitters", year = "2009", title = "A Topos for Algebraic Quantum Theory", journal = "Communications in Mathematical Physics", volume = "291", number = "1", pages = "63--110", doi = "10.1007/s00220-009-0865-6", ) @unpublished(HeunenLandsmanSpitters:Bohrn, author = "Chris Heunen and Nicolaas P. Landsman and Bas Spitters", year = "2010", title = "{B}ohrification of Operator Algebras and Quantum Logic", note = "ArXiv:quant-ph/0905.2275v4", ) @article(IshamBfield:ToposPKST1, author = "C.J. Isham and J. Butterfield", year = "1998", title = "Topos Perspectives on the {K}ochen-{S}pecker {T}heorem {I}. Quantum States as Generalized Valuations", journal = "International Journal of Theoretical Physics", volume = "37", number = "11", pages = "2669--2733", doi = "10.1023/A:1026680806775", ) @article(IshamBfield:ToposPKST2, author = "C.J. Isham and J. Butterfield", year = "1999", title = "Topos Perspectives on the {K}ochen-{S}pecker {T}heorem {I}{I}. Conceptual Aspects and Classical Analogues", journal = "International Journal of Theoretical Physics", volume = "38", number = "3", pages = "827--859", doi = "10.1023/A:1026652817988", ) @article(Jo:FibPP, author = "P.T. Johnstone", year = "1993", title = "Fibrations and Partial Products in a 2-category", journal = "Applied Categorical Structures", volume = "1", pages = "141--179", doi = "10.1007/BF00880041", ) @inproceedings(JonesPlot:ProbPower, author = "C. Jones and G. Plotkin", year = "1989", title = "A Probabilistic Powerdomain of Evaluations", booktitle = "LICS '89", publisher = "IEEE Computer Society Press", pages = "186--195", ) @article(JoyalTier, author = "A. Joyal and M. Tierney", year = "1984", title = "An Extension of the {G}alois Theory of {G}rothendieck", journal = "Memoirs of the American Mathematical Society", volume = "309", ) @article(KochenSpecker, author = "Simon Kochen and Ernst Specker", year = "1967", title = "{The problem of hidden variables in quantum mechanics}", journal = "Journal of Mathematics and Mechanics", volume = "17", pages = "59--87", ) @inproceedings(Spitters:SpaceMOSNCA, author = "Bas Spitters", year = "2010", title = "The space of Measurement Outcomes as a Spectrum for Non-Commutative Algebras", editor = "S. Barry Cooper and Prakash Panangaden and Elham Kashefi", booktitle = "Proceedings Sixth Workshop on Developments in Computational Models: Causality, Computation, and Physics (DCM 2010)", series = "Electronic Proceedings in Theoretical Computer Science", volume = "26", pages = "127--134", doi = "10.4204/EPTCS.26.12", ) @inproceedings(Street, author = "Ross Street", year = "1974", title = "Fibrations and {Y}oneda's Lemma in a 2-category", editor = "G.M. Kelly", booktitle = "Category Seminar Sydney 1972/73", series = "Lecture Notes in Mathematics", volume = "420", pages = "104--133", ) @article(Integration, author = "Steven Vickers", year = "2008", title = "A Localic Theory of Lower and Upper Integrals", journal = "Mathematical Logic Quarterly", volume = "54", number = "1", pages = "109--123", doi = "10.1002/malq.200710028", ) @unpublished(Vickers:ContIsGeom, author = "Steven Vickers", year = "2011", title = "Continuity is Geometricity", note = "Talk given at workshop ``Logic, Categories, Semantics'' at Bordeaux, November 2010. Preprint at \url {http://www.cs.bham.ac.uk/~sjv/GeoAspects.pdf}", ) @unpublished(Vickers:Riesz, author = "Steven Vickers", year = "2011", title = "A Monad of Valuation Locales", note = "Preprint at \url {http://www.cs.bham.ac.uk/~sjv/Riesz.pdf}", )