$MV$-test spaces versus $MV$-algebras
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 1, pp. 189-203 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In analogy with effect algebras, we introduce the test spaces and $MV$-test spaces. A test corresponds to a hypothesis on the propositional system, or, equivalently, to a partition of unity. We show that there is a close correspondence between $MV$-algebras and $MV$-test spaces.
In analogy with effect algebras, we introduce the test spaces and $MV$-test spaces. A test corresponds to a hypothesis on the propositional system, or, equivalently, to a partition of unity. We show that there is a close correspondence between $MV$-algebras and $MV$-test spaces.
Classification : 03B50, 03G12, 06D35
Keywords: algebra; effect algebra; $MV$-algebra; test space; $MV$-test space; state; weight
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Nola, Antonio Di; Dvurečenskij, Anatolij. $MV$-test spaces versus $MV$-algebras. Czechoslovak Mathematical Journal, Tome 54 (2004) no. 1, pp. 189-203. http://geodesic.mathdoc.fr/item/CMJ_2004_54_1_a16/

[1] P. Busch, P. J. Lahti and P. Mittelstaedt: The Quantum Theory of Measurement. Lecture Notes in Physics. Springer-Verlag, Berlin-Heidelberg-New York-London-Budapest, 1991. | MR

[2] C. C.  Chang: Algebraic analysis of many valued logics. Trans. Amer. Math. Soc. 88 (1958), 467–490. | DOI | MR | Zbl

[3] R.  Cignoli, I. M. L.  D’Ottaviano and D.  Mundici: Algebraic Foundations of Many-Valued Reasoning. Kluwer Academic Publ., Dordrecht, 2000. | MR

[4] F.  Chovanec: States and observables on $MV$-algebras. Tatra Mt. Math. Publ. 3 (1993), 55–65. | MR | Zbl

[5] A.  Dvurečenskij and S.  Pulmannová: D-test spaces and difference posets. Rep. Math. Phys. 34 (1994), 151–170. | DOI | MR

[6] A.  Dvurečenskij and S.  Pulmannová: New Trends in Quantum Structures. Kluwer Acad. Publ., Dordrecht, Ister Science, Bratislava, 2000. | MR

[7] A.  Dvurečenskij and T.  Vetterlein: Pseudoeffect algebras. I.  Basic properties. Inter. J.  Theor. Phys. 40 (2001), 685–701. | MR

[8] A.  Dvurečenskij and T.  Vetterlein: Pseudoeffect algebras. II.  Group representations. Inter. J.  Theor. Phys. 40 (2001), 703–726. | MR

[9] D. J.  Foulis and M. K.  Bennett: Effect algebras and unsharp quantum logics. Found. Phys. 24 (1994), 1325–1346. | DOI | MR

[10] D. J.  Foulis and C. H.  Randall: Operational statistics. I.  Basic concepts. J.  Math. Phys. 13 (1972), 1667–1675. | DOI | MR

[11] S.  Gudder: Effect test spaces. Inter. J.  Theor. Phys. 36 (1997), 2681–2705. | MR | Zbl

[12] A. N.  Kolmogorov: Grundbegriffe der Wahrscheinlichkeitsrechnung. Berlin, 1933. | Zbl

[13] D.  Mundici: Interpretation of $AF$ $C^*$-algebras in Łukasiewicz sentential calculus. J.  Funct. Anal. 65 (1986), 15–63. | DOI | MR | Zbl

[14] D.  Mundici: Averaging the truth-value in Łukasiewicz logic. Studia Logica 55 (1995), 113–127. | DOI | MR | Zbl

[15] D.  Mundici: Reasoning on imprecisely defined functions. In: Discovering the World with Fuzzy Logic. Studies in Fuzziness and Soft Computing, V.  Novák, I.  Perfilieva (eds.), Physica-Verlag, Berlin, 2000, pp. 331–366. | MR | Zbl

[16] Z.  Riečanová: A generalization of blocks for lattice effect algebras. Inter. J.  Theoret. Phys. 39 (2000), 231–237. | MR

[17] B.  Riečan and D.  Mundici: Probability on $MV$-algebras. In: Handbook of Measure Theory, E.  Pap (ed.), North-Holland, Amsterdam, 2002, pp. 869–910. | MR