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2003 | 23 | 1 | 63-79
Tytuł artykułu

Effect algebras and ring-like structures

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The dichotomic physical quantities, also called propositions, can be naturally associated to maps of the set of states into the real interval [0,1]. We show that the structure of effect algebra associated to such maps can be represented by quasiring structures, which are a generalization of Boolean rings, in such a way that the ring operation of addition can be non-associative and the ring multiplication non-distributive with respect to addition. By some natural assumption on the effect algebra, the associativity of the ring addition implies the distributivity of the lattice structure corresponding to the effect algebra. This can be interpreted as another characterization of the classicality of the logical systems of propositions, independent of the characterizations by Bell-like inequalities.
Twórcy
  • Department of Physics, University of Genova and Istituto Nazionale di Fisica Nucleare, Sezione di Genova, via Dodecaneso 33, I-16146 Genova, Italy
  • Faculty of Mathematics and Information Science, Warsaw University of Technology, Plac Politechniki 1, PL 00 661 Warsaw, Poland
Bibliografia
  • [1] E.G. Beltrametti and M.J. Maczyński, On a characterization of classical and non-classical probabilities, J. Math. Phys. 32 (1991), 1280-1286.
  • [2] E.G. Beltrametti and M.J. Maczyński, On the range of non-classical probability, Rep. Math. Phys. 36 (1995), 195-213.
  • [3] E.G. Beltrametti and S. Bugajski, Effect algebras and statistical theories, J. Math. Phys. 38 (1997), 3020-3030.
  • [4] E.G. Beltrametti, S. Bugajski and V.S. Varadarajan, Extensions of convexity models, J. Math. Phys. 41 (2000). doi: 1415-1429
  • [5] D. Dorninger, H. Länger and M. Maczyński, On ring-like structures induced by Mackey's probability function, Rep. Math. Phys. 43 (1999), 499-515.
  • [6] R. Sikorski, Boolean Algebras, 2nd ed., Springer-Verlag, Berlin-Heidelberg-New York 1964.
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1064
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