- Tytuł:
- Probability measures and logical connectives on quantum logics
- Autorzy:
-
Nánásiová, Oľga
Valášková, Ľubica
Čerňanová, Viera - Powiązania:
- https://bibliotekanauki.pl/articles/384839.pdf
- Data publikacji:
- 2019
- Wydawca:
- Sieć Badawcza Łukasiewicz - Przemysłowy Instytut Automatyki i Pomiarów
- Tematy:
-
logical connectives
orthomodular lattice
quantum logic
probability measure
state - Opis:
- The present paper is devoted to modelling of a probabi‐ lity measure of logical connectives on a quantum logic via a G‐map, which is a special map on it. We follow the work in which the probability of logical conjunction (AND), dis‐ junction (OR), symmetric difference (XOR) and their nega‐ tions for non‐compatible propositions are studied. Now we study all remaining cases of G‐maps on quantum lo‐ gic, namely a probability measure of projections, of impli‐ cations, and of their negations. We show that unlike clas‐ sical (Boolean) logic, probability measures of projections on a quantum logic are not necessarilly pure projections. We indicate how it is possible to define a probability me‐ asure of implication using a G‐map in the quantum logic, and then we study some properties of this measure which are different from a measure of implication in a Boolean algebra. Finally, we compare the properties of a G‐map with the properties of a probability measure related to logical connectives on a Boolean algebra.
- Źródło:
-
Journal of Automation Mobile Robotics and Intelligent Systems; 2019, 13, 3; 64-73
1897-8649
2080-2145 - Pojawia się w:
- Journal of Automation Mobile Robotics and Intelligent Systems
- Dostawca treści:
- Biblioteka Nauki
Artykuł