# Partial and unsharp quantum logics

@article{Chiara1994PartialAU, title={Partial and unsharp quantum logics}, author={M. Chiara and R. Giuntini}, journal={Foundations of Physics}, year={1994}, volume={24}, pages={1161-1177} }

The total and the sharp character of orthodox quantum logic has been put in question in different contexts. This paper presents the basic ideas for a unified approach to partial and unsharp forms of quantum logic. We prove a completeness theorem for some partial logics based on orthoalgebras and orthomodular posets. We introduce the notion of unsharp orthoalgebra and of generalized MV algebra. The class of all effects of any Hilbert space gives rise to particular examples of these structures… Expand

#### 28 Citations

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It is proved that the category of unsharp orthoalgebras is isomorphic to the categories of D-posets and a completeness theorem for some partial logics based on unsharp Ortho-Algebra, ortho-alge Bras and orthomodular posets is proved. Expand

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The algebraic structures arising in the axiomatic framework of unsharp quantummechanics based on effect operators on a Hilbert space are investigated. It isstressed that usually considered “effect”… Expand

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An abstract investigation about quantum histories naturally meets ideas that have been developed in the framework of dynamic logic [5], where possible relations between truths and actions are… Expand

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This chapter discusses the Birkhoff-von Neumann idea of quantum logic, which is related to deep mathematical discoveries in the mid thirties, to the history of quantum mechanics in the twenties, and to conceptual difficulties in connection with the frequency-interpretation of quantum probability. Expand

Łukasiewicz Operations in Fuzzy Set and Many-Valued Representations of Quantum Logics

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It, is shown that Birkhoff –von Neumann quantum logic (i.e., an orthomodular lattice or poset) possessing an ordering set of probability measures S can be isomorphically represented as a family of… Expand

Quantum Physics and Classical Physics—In the Light of Quantum Logic

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In contrast to the Copenhagen interpretation we consider quantum mechanics as universally valid and query whether classical physics is really intuitive and plausible. We discuss these problems within… Expand

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The debate about constructivism in physics (and in quantum mechanics, in particular) has led to different kinds of questions that can be conventionally framed in two classes. One concerns the… Expand

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