The Logics of Orthoalgebras

The notion of unsharp orthoalgebra is introduced and it is proved that the category of unsharp orthoalgebras is isomorphic to the category of D-posets. A completeness theorem for some partial logics based on unsharp orthoalgebras, orthoalgebras and orthomodular posets is proved.

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Bibliographic Details
Published in:Studia logica 1995-07, Vol.55 (1), p.3-22
Main Authors: Chiara, Maria Luisa Dalla, Giuntini, Roberto
Format: Article
Language:English
Subjects:
Excluded middle
Hilbert spaces
Logical disjunction
Logical theorems
Model theory
Morphisms
Partially ordered sets
Quantum logic
Quantum mechanics
Semantics
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Description
Summary:The notion of unsharp orthoalgebra is introduced and it is proved that the category of unsharp orthoalgebras is isomorphic to the category of D-posets. A completeness theorem for some partial logics based on unsharp orthoalgebras, orthoalgebras and orthomodular posets is proved.
ISSN:0039-3215
1572-8730
DOI:10.1007/BF01053029