Abstract : This paper describes some basic relationships between mathematical structures that are relevant in quantum logic and probability, namely convex sets, effect algebras, and a new class of functors that we call 'convex functors'; they include what are usually called probability distribution functors. These relationships take the form of three adjunctions. Two of these three are 'dual' adjunctions for convex sets, one time with the Boolean truth values {0,1} as dualising object, and one time with the probablity values [0,1]. The third adjunction is between effect algebras and convex functors.
Type de document :
Communication dans un congrès
Cristian S. Calude; Vladimiro Sassone. 6th IFIP TC 1/WG 2.2 International Conference on Theoretical Computer Science (TCS) / Held as Part of World Computer Congress (WCC), Sep 2010, Brisbane, Australia. Springer, IFIP Advances in Information and Communication Technology, AICT-323, pp.1-19, 2010, Theoretical Computer Science. 〈10.1007/978-3-642-15240-5_1〉
https://hal.inria.fr/hal-01054454
Contributeur : Hal Ifip
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Soumis le : mercredi 6 août 2014 - 16:24:59
Dernière modification le : mercredi 9 août 2017 - 12:03:27
Document(s) archivé(s) le : mercredi 26 novembre 2014 - 00:58:21
Bart Jacobs. Convexity, Duality and Effects. Cristian S. Calude; Vladimiro Sassone. 6th IFIP TC 1/WG 2.2 International Conference on Theoretical Computer Science (TCS) / Held as Part of World Computer Congress (WCC), Sep 2010, Brisbane, Australia. Springer, IFIP Advances in Information and Communication Technology, AICT-323, pp.1-19, 2010, Theoretical Computer Science. 〈10.1007/978-3-642-15240-5_1〉. 〈hal-01054454〉
