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Applications of Mathematics
Article . 1985 . Peer-reviewed
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On the concreteness of quantum logics

Authors: Pavel Pták; John David Maitland Wright;

On the concreteness of quantum logics

Abstract

The authors take the very conventional view of quantum logic as an orthomodular poset and conduct a very traditional enquiry into its relation to classical Boolean logic. That is, they attempt to find a natural relation between the structure of this orthomodular poset and the classical structure of a subset of sets. The meagreness of their results should serve to show that this traditional approach has proved unfruitful. The authors do not attempt to relate their discussion to quantum mechanics. In fact the authors establish a relation between the ''centres'', i.e. the globally compatible elements, of the orthomodular posets and the centres of ''concrete'' logics, i.e. of orthocomplemented posets with 1 and 0 which are isomorphic to a collection of subsets of a set. This result will probably be of interest only to the most devoted ''quantum logicians''. They also, perhaps more interestingly, establish an embedding of orthocomplemented posets into concrete logics.

Keywords

orthomodular poset, orthomodular lattice, centres, orthocomplemented posets, concrete logics, Quantum logic

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
8
Average
Top 10%
Average
bronze