Classical Logic and Quantum Logic with Multiple and Common Lattice Models
Author
Source
Advances in Mathematical Physics
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-09-01
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
We consider a proper propositional quantum logic and show that it has multiple disjoint lattice models, only one of which is an orthomodular lattice (algebra) underlying Hilbert (quantum) space.
We give an equivalent proof for the classical logic which turns out to have disjoint distributive and nondistributive ortholattices.
In particular, we prove that both classical logic and quantum logic are sound and complete with respect to each of these lattices.
We also show that there is one common nonorthomodular lattice that is a model of both quantum and classical logic.
In technical terms, that enables us to run the same classical logic on both a digital (standard, two-subset, 0-1-bit) computer and a nondigital (say, a six-subset) computer (with appropriate chips and circuits).
With quantum logic, the same six-element common lattice can serve us as a benchmark for an efficient evaluation of equations of bigger lattice models or theorems of the logic.
American Psychological Association (APA)
Pavičić, Mladen. 2016. Classical Logic and Quantum Logic with Multiple and Common Lattice Models. Advances in Mathematical Physics،Vol. 2016, no. 2016, pp.1-12.
https://search.emarefa.net/detail/BIM-1095876
Modern Language Association (MLA)
Pavičić, Mladen. Classical Logic and Quantum Logic with Multiple and Common Lattice Models. Advances in Mathematical Physics No. 2016 (2016), pp.1-12.
https://search.emarefa.net/detail/BIM-1095876
American Medical Association (AMA)
Pavičić, Mladen. Classical Logic and Quantum Logic with Multiple and Common Lattice Models. Advances in Mathematical Physics. 2016. Vol. 2016, no. 2016, pp.1-12.
https://search.emarefa.net/detail/BIM-1095876
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1095876