Algebras of measurements: The logical structure of quantum mechanics

Daniel Lehmann, Kurt Engesser, Dov M. Gabbay

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


In quantum physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties of such operators are justified on epistemological grounds. Commutation of measurements is a central topic of interest. Classical logical systems may be viewed as measurement algebras in which all measurements commute.

Original languageEnglish
Pages (from-to)715-741
Number of pages27
JournalInternational Journal of Theoretical Physics
Issue number4
StatePublished - Apr 2006
Externally publishedYes

Bibliographical note

Funding Information:
This work was partially supported by the Jean and Helene Alfassa fund for research in Artificial Intelligence, by the Israel Science Foundation grant 183/03 on “Quantum and other cumulative logics” and by EPSRC Visiting Fellowship GR/T 24562 on “Quantum Logic.”


  • Measurement algebras
  • Quantum logic
  • Quantum measurements


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