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Classical Logic and Quantum Logic with Multiple and Common Lattice Models (CROSBI ID 231022)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Pavičić, Mladen Classical Logic and Quantum Logic with Multiple and Common Lattice Models // Advances in Mathematical Physics, 2016 (2016), 6830685-1-6830685-12. doi: 10.1155/2016/6830685

Podaci o odgovornosti

Pavičić, Mladen

engleski

Classical Logic and Quantum Logic with Multiple and Common Lattice Models

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.

quantum logic ; classical logic ; model theory ; orthomodular lattices ; weakly orthomodular lattices ; distributive lattices ; weakly distributive lattices

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Podaci o izdanju

2016

2016.

6830685-1-6830685-12

objavljeno

1687-9120

10.1155/2016/6830685

Povezanost rada

Fizika

Poveznice
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