Structural Properties of Algebras of S-probabilities

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F18%3A73587182" target="_blank" >RIV/61989592:15310/18:73587182 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1515/ms-2017-0118" target="_blank" >http://dx.doi.org/10.1515/ms-2017-0118</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/ms-2017-0118" target="_blank" >10.1515/ms-2017-0118</a>

Result language
angličtina
Original language name
Structural Properties of Algebras of S-probabilities
Original language description
Let S be a set of states of a physical system. The probabilities p(s) of the occurrence of an event when the system is in different states s in S define a function from S to [0; 1] called a numerical event or, more precisely, an S-probability. A set of S-probabilities comprising the constant functions 0 and 1 which is structured by means of the addition and order of real functions in such a way that an orthomodular partially ordered set arises is called an algebra of S-probabilities, a structure significant as a quantum-logic with a full set of states. The main goal of this paper is to describe algebraic properties of algebras of S-probabilities through operations with real functions. In particular, we describe lattice characteristics and characterize Boolean features. Moreover, representations by sets are considered and pertinent examples provided.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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