@book(Alfsen71, author = "E. Alfsen", year = "1971", title = "Compact Convex Sets and Boundary Integrals", publisher = "Springer-Verlag", doi = "10.1007/978-3-642-65009-3", ) @article(BirkhoffN36, author = "George D. Birkhoff and John von Neumann", year = "1936", title = "The logic of quantum mechanics", journal = "Annals of Math.", volume = "37", pages = "823--834", doi = "10.2307/1968621", ) @article(Busch03, author = "P. Busch", year = "2003", title = "Quantum states and generalized observables: a simple proof of {G}leason's theorem", journal = "Phys. Rev. Lett.", volume = "91", number = "12", doi = "10.1103/PhysRevLett.91.120403", ) @article(HondtP06, author = "E. D'Hondt and P. Panangaden", year = "2006", title = "Quantum weakest preconditions", journal = "Math. Struct. in Comp. Sci.", volume = "16", number = "3", pages = "429--451", doi = "10.1017/S0960129506005251", ) @book(DiestelU77, author = "J. Diestel and J. Uhl", year = "1977", title = "Vector Measures", publisher = "American Mathematical Society", doi = "10.1090/surv/015", ) @book(DvurecenskijP00, author = "A. Dvure\v {c}enskij and S. Pulmannov{\'a}", year = "2000", title = "New Trends in Quantum Structures", publisher = "Kluwer Acad. Publ.", address = "Dordrecht", doi = "10.1007/978-94-017-2422-7", ) @article(FoulisB94, author = "D. J. Foulis and M.K. Bennett", year = "1994", title = "Effect Algebras and Unsharp Quantum Logics", journal = "Found. Phys.", volume = "24", number = "10", pages = "1331--1352", doi = "10.1007/BF02283036", ) @incollection(Giry82, author = "M. Giry", year = "1982", title = "A categorical approach to probability theory", editor = "B. Banaschewski", booktitle = "Categorical Aspects of Topology and Analysis", series = "Lecture Notes in Mathematics", volume = "915", publisher = "Springer Berlin Heidelberg", pages = "68--85", doi = "10.1007/BFb0092872", ) @article(Gudder98, author = "S. Gudder", year = "1998", title = "Morphisms, tensor products and $\sigma $-effect algebras", journal = "Rep. Math. Phys.", volume = "42", number = "3", pages = "321--346", doi = "10.1016/S0034-4877(99)80003-2", ) @article(Gudder10, author = "S. Gudder", year = "2010", title = "Sequential product of quantum effects: an overview", journal = "Int. J. Math. Phys.", volume = "49", pages = "3118--3130", doi = "10.1007/s10773-010-0390-6", ) @article(GudderG02, author = "S. Gudder and R. Greechie", year = "2002", title = "Sequential products on effect algebras", journal = "Rep. Math. Phys.", volume = "49", pages = "87--111", doi = "10.1016/S0034-4877(02)80007-6", ) @article(GudderN01, author = "S. Gudder and G. Nagy", year = "2001", title = "Sequential quantum measurements", journal = "J. Math. Phys.", volume = "42", number = "11", pages = "5212--5222", doi = "10.1063/1.1407837", ) @article(GudderP98, author = "S. Gudder and S. Pulmannov\'{a}", year = "1998", title = "Representation theorem for convex effect algebras", journal = "Commentationes Mathematicae Universitatis Carolinae", volume = "39", number = "4", pages = "645--659", ) @book(HeinosaariZ12, author = "T. Heinosaari and M. Ziman", year = "2012", title = "The Mathematical Language of Quantum Theory. From Uncertainty to Entanglement", publisher = "Cambridge Univ. Press", ) @misc(Jacobs12, author = "B. Jacobs", year = "2012", title = "New directions in categorical logic, for classical, probabilistic, and quantum logic", note = "\url {http://arxiv.org/abs/1205.3940}", ) @misc(Jacobs13, author = "B. Jacobs", year = "2013", title = "Measurable Spaces and their Effect Logic", note = "Logic in Computer Science (LICS 2013)", ) @inproceedings(JacobsM12b, author = "B. Jacobs and J. Mandemaker", year = "2012", title = "The Expectation Monad in Quantum Foundations", editor = "B. Jacobs and P. Selinger and B. Spitters", booktitle = "Quantum Physics and Logic (QPL) 2011", series = "Elect. Proc. in Theor. Comp. Sci.", volume = "95", pages = "143--182", ) @incollection(JacobsM12c, author = "B. Jacobs and J. Mandemaker", year = "2012", title = "Relating Operator Spaces via Adjunctions", editor = "J. Chubb Reimann and V. Harizanov and A. Eskandarian", booktitle = "Logic and Algebraic Structures in Quantum Computing and Information", series = "Lect. Notes in Logic", publisher = "Cambridge Univ. Press", note = "See arxiv.org/abs/1201.1272", ) @book(KadisonR83, author = "R. Kadison and J. Ringrose", year = "1983", title = "Fundamentals of the Theory of Operator Algebras", publisher = "Academic Press", ) @book(Landsman98, author = "N. Landsman", year = "1998", title = "Mathematical Topics Between Classical and Quantum Mechanics", publisher = "Springer", doi = "10.1007/978-1-4612-1680-3", ) @incollection(Nagel74, author = "R. Nagel", year = "1974", title = "Order unit and base norm spaces", editor = "A. Hartk\"amper and H. Neumann", booktitle = "Foundations of Quantum Mechanics and Ordered Linear Spaces", series = "Lecture Notes in Physics", volume = "29", publisher = "Springer Berlin Heidelberg", pages = "23--29", doi = "10.1007/3-540-06725-6-4", ) @book(Schroeck96, author = "F. Schroeck", year = "1996", title = "Quantum Mechanics on Phase Space", publisher = "Kluwer Acad. Publ.", doi = "10.1007/978-94-017-2830-0", )