Partial quantum logics revisited

International Journal of General Systems

Volumn 40, Issue 1, 2011, Pages 23-38

  Vetterlein, Thomas ^a  

^a MEDICAL UNIVERSITY OF VIENNA   (Austria)

Author keywords

Hilbert space; partial Boolean algebras; partial MV algebras; quantum logic

Indexed keywords

ALGEBRAIC APPROACHES; ALGEBRAIC MODELS; AUTOMORPHISMS; CLOSED SUBSPACE; FOUNDATIONAL PROBLEMS; MV-ALGEBRAS; ORTHOMODULAR LATTICES; PARTIAL BOOLEAN ALGEBRAS; QUANTUM LOGIC; QUANTUM PHYSICS; REPRESENTATION THEORY;

HILBERT SPACES; QUANTUM ELECTRONICS; QUANTUM OPTICS;

BOOLEAN ALGEBRA;

EID: 78649503006     PISSN: 03081079     EISSN: 15635104     Source Type: Journal    
DOI: 10.1080/03081079.2010.505030     Document Type: Article

References (12)

1. Cignoli, R., D'Ottaviano, I. M. L. and Mundici, D., 2000. Algebraic foundations of many-valued reasoning. Dordrecht: Kluwer Academic Publisher.
2. Czelakowski, J., 1974. Logics based on partial Boolean δ-algebras. I. Student log, 33, 371-396.
3. Dalla Chiara, M. L. and Giuntini, R., 1995. The logics of orthoalgebras. Studia logica, 55, 3-22.
4. Dvurečenskij, A. and Pulmannová, S., 2000. New trends in quantum structures. Dordrecht: Kluwer Academic Publisher and Bratislava: Ister Science.
5. Foulis, D. J. and Bennett, M. K., 1994. Effect algebras and unsharp quantum logics. Foundations of physics, 24, 1325-1346.
6. Kochen, S. and Specker, E. P., 1965. Logical structures arising in quantum theory. In: J. Addison, L. Henkin and A. Tarski, eds. Theory of models. Amsterdam: North-Holland, 177-189.
7. Lubotzky, A., 1988. A group theoretic characterization of linear groups. Journal of algebra, 113, 207-214.
8. Mayet, R., 1998. Some characterizations of the underlying division ring of a Hilbert lattice by automorphisms. International journal of theoritical physics, 37, 109-114.
9. Mayet, R. and Pulmannová, S., 1994. Nearly orthosymmetric ortholattices and Hilbert spaces. Foundation of physics, 24, 1425-1437.
10. Metcalfe, G., Olivetti, N. and Gabbay, D., 2002. Analytic sequent calculi for Abelian and Łukasiewicz logics. In: U. Egly, et al., eds. Automated reasoning with analytic tableaux and related methods. Proceeding of the 11th conference TABLEAUX (Copenhagen 2002). Berlin: Springer-Verlag, 191-205.
11. Pedersen, G. K., 1989. Analysis now. New York: Springer-Verlag.
12. Solèr, M. P., 1995. Characterization of Hilbert spaces by orthomodular spaces. Communication algebra, 23, 219-243.