Probability Measures and Projections on Quantum Logics

  • Oľga NánásiováEmail author
  • Viera Čerňanová
  • Ľubica Valášková
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 945)


The present paper is devoted to modelling of a probability measure of logical connectives on a quantum logic (QL), via a G-map, which is a special map on it. We follow the work in which the probability of logical conjunction, disjunction and symmetric difference and their negations for non-compatible propositions are studied.

We study such a G-map on quantum logics, which is a probability measure of a projection and show, that unlike classical (Boolean) logic, probability measure of projections on a quantum logic are not necessarilly pure projections.

We compare properties of a G-map on QLs with properties of a probability measure related to logical connectives on a Boolean algebra.


Logical connectives Orthomodular lattice Quantum logic Probability measure State 



The author (O. Nánásiová) would like to thank for the support of the VEGA grant agency by means of grant VEGA 1/0710/15 and VEGA 1/0159/17 and the author (L. Valášková) would like to thank for the support of VEGA 1/0420/15.


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Oľga Nánásiová
    • 1
    Email author
  • Viera Čerňanová
    • 2
  • Ľubica Valášková
    • 3
  1. 1.Institute of Computer Science and MathematicsSlovak University of TechnologyBratislavaSlovakia
  2. 2.Department of Mathematics and Computer Science, Faculty of EducationTrnava UniversityTrnavaSlovakia
  3. 3.Department of Mathematics and Descriptive GeometrySlovak University of TechnologyBratislavaSlovakia

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