Naslov
Classical Logic and Quantum Logic with Multiple and Common Lattice Models

Autori
Pavičić, Mladen

Izvornik
Advances in Mathematical Physics (1687-9120) 2016 (2016); 6830685-1

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

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

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Fizika

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