Dorninger, D., & Länger, H. (2023). On ring-like event systems in quantum logic. Asian-European Journal of Mathematics, 16(8), Article 2350148. https://doi.org/10.1142/S1793557123501486
E104 - Institut für Diskrete Mathematik und Geometrie E104-01 - Forschungsbereich Algebra
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Journal:
Asian-European Journal of Mathematics
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ISSN:
1793-5571
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Date (published):
Aug-2023
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Number of Pages:
14
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Publisher:
World Scientific Publishing
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Peer reviewed:
Yes
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Keywords:
quantum logic; orthomodular lattice; ring-like structure of events; numerical event
en
Abstract:
A class of ring-like structures of events (RLSEs) is studied that generalizes Boolean rings. Quantum logics represented by orthomodular lattices are characterized within this class and the correspondence between Boolean algebras and Boolean rings is enlarged to orthomodular lattices. The structure of RLSEs and various subclasses is analyzed and classical logics are especially identified. Moreover, sets of numerical events within different contexts of physical problems are described. A numerical event is defined as a function p from a set S of states of a physical system to [0,1] such that p(s) is the probability of the occurrence of an event when the system is in state s∈S. In particular, the question is answered whether a given (small) set of numerical events will give rise to the assumption that one deals with a classical physical system or a quantum-mechanical one.
