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Affine Maczyński logics on compact convex sets of states

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Abstract

Sets of affine functions satisfying Maczyński orthogonality postulate and defined on compact convex sets of states are examined. Relations between affine Maski logics and Boolean algebras when the set of states is a Bauer simplex (classical mechanics, some models of nonlinear quantum mechanics) are studied. It is shown that an affine Maczyński logic defined on a Bauer simplex is a Boolean algebra if it is a sublattice of a lattice consisting of all bounded affine functions defined on the simplex.

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Authors and Affiliations

  1. Institute of Mathematics, University of Gdańsk, 80-952, Gdańsk, Poland

    J. Pykacz

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  1. J. Pykacz
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Pykacz, J. Affine Maczyński logics on compact convex sets of states. Int J Theor Phys 22, 97–106 (1983). https://doi.org/10.1007/BF02082526

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  • DOI: https://doi.org/10.1007/BF02082526

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