M V -test spaces versus M V -algebras

Antonio Di Nola; Anatolij Dvurečenskij

Czechoslovak Mathematical Journal (2004)

  • Volume: 54, Issue: 1, page 189-203
  • ISSN: 0011-4642

Abstract

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In analogy with effect algebras, we introduce the test spaces and M V -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 M V -algebras and M V -test spaces.

How to cite

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Nola, Antonio Di, and Dvurečenskij, Anatolij. "$MV$-test spaces versus $MV$-algebras." Czechoslovak Mathematical Journal 54.1 (2004): 189-203. <http://eudml.org/doc/30849>.

@article{Nola2004,
abstract = {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.},
author = {Nola, Antonio Di, Dvurečenskij, Anatolij},
journal = {Czechoslovak Mathematical Journal},
keywords = {algebra; effect algebra; $MV$-algebra; test space; $MV$-test space; state; weight; effect algebra; MV-algebra; MV-test space; state; weight},
language = {eng},
number = {1},
pages = {189-203},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {$MV$-test spaces versus $MV$-algebras},
url = {http://eudml.org/doc/30849},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Nola, Antonio Di
AU - Dvurečenskij, Anatolij
TI - $MV$-test spaces versus $MV$-algebras
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 1
SP - 189
EP - 203
AB - 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.
LA - eng
KW - algebra; effect algebra; $MV$-algebra; test space; $MV$-test space; state; weight; effect algebra; MV-algebra; MV-test space; state; weight
UR - http://eudml.org/doc/30849
ER -

References

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  1. The Quantum Theory of Measurement. Lecture Notes in Physics, Springer-Verlag, Berlin-Heidelberg-New York-London-Budapest, 1991. (1991) MR1176754
  2. 10.1090/S0002-9947-1958-0094302-9, Trans. Amer. Math. Soc. 88 (1958), 467–490. (1958) Zbl0084.00704MR0094302DOI10.1090/S0002-9947-1958-0094302-9
  3. Algebraic Foundations of Many-Valued Reasoning, Kluwer Academic Publ., Dordrecht, 2000. (2000) MR1786097
  4. States and observables on M V -algebras, Tatra Mt. Math. Publ. 3 (1993), 55–65. (1993) Zbl0799.03074MR1278519
  5. 10.1016/0034-4877(94)90034-5, Rep. Math. Phys. 34 (1994), 151–170. (1994) MR1323126DOI10.1016/0034-4877(94)90034-5
  6. New Trends in Quantum Structures, Kluwer Acad. Publ., Dordrecht, Ister Science, Bratislava, 2000. (2000) MR1861369
  7. Pseudoeffect algebras. I.  Basic properties, Inter. J.  Theor. Phys. 40 (2001), 685–701. (2001) MR1831592
  8. Pseudoeffect algebras. II.  Group representations, Inter. J.  Theor. Phys. 40 (2001), 703–726. (2001) MR1831593
  9. 10.1007/BF02283036, Found. Phys. 24 (1994), 1325–1346. (1994) MR1304942DOI10.1007/BF02283036
  10. 10.1063/1.1665890, J.  Math. Phys. 13 (1972), 1667–1675. (1972) MR0416417DOI10.1063/1.1665890
  11. Effect test spaces, Inter. J.  Theor. Phys. 36 (1997), 2681–2705. (1997) Zbl0946.81006MR1614188
  12. Grundbegriffe der Wahrscheinlichkeitsrechnung, , Berlin, 1933. (1933) Zbl0007.21601
  13. 10.1016/0022-1236(86)90015-7, J.  Funct. Anal. 65 (1986), 15–63. (1986) Zbl0597.46059MR0819173DOI10.1016/0022-1236(86)90015-7
  14. 10.1007/BF01053035, Studia Logica 55 (1995), 113–127. (1995) Zbl0836.03016MR1348840DOI10.1007/BF01053035
  15. 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. (2000) Zbl1007.03024MR1858107
  16. A generalization of blocks for lattice effect algebras, Inter. J.  Theoret. Phys. 39 (2000), 231–237. (2000) MR1762594
  17. Probability on M V -algebras, In: Handbook of Measure Theory, E.  Pap (ed.), North-Holland, Amsterdam, 2002, pp. 869–910. (2002) MR1954631

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