dorsal/arxiv
View SchemaModel-Theoretic Investigations into Consequence Operation (Cn) in Quantum Logics. An Algebraic Approach
| Authors | Piotr Wilczek |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0507209 |
| URL | https://arxiv.org/abs/quant-ph/0507209 |
| DOI | 10.1007/s10773-006-9060-0 |
| Journal | International Journal of Theoretical Physics, 45, No. 4, 695-705 (2006) |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
In this paper we present the fundamentals of the so-called algebraic approach to propositional quantum logics. We define the set of formulas describing quantum reality as a free algebra freely generated by the set of quantum propositional variables. We define the general notion of logic as a structural consequence operation. Next we introduce the concept of logical matrices understood as a models of quantum logics. We give the definitions of two quantum consequence operations defined in these models.
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"abstract": "In this paper we present the fundamentals of the so-called algebraic approach\nto propositional quantum logics. We define the set of formulas describing\nquantum reality as a free algebra freely generated by the set of quantum\npropositional variables. We define the general notion of logic as a structural\nconsequence operation. Next we introduce the concept of logical matrices\nunderstood as a models of quantum logics. We give the definitions of two\nquantum consequence operations defined in these models.",
"arxiv_id": "quant-ph/0507209",
"authors": [
"Piotr Wilczek"
],
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"quant-ph"
],
"doi": "10.1007/s10773-006-9060-0",
"journal_ref": "International Journal of Theoretical Physics, 45, No. 4, 695-705\n (2006)",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Model-Theoretic Investigations into Consequence Operation (Cn) in Quantum Logics. An Algebraic Approach",
"url": "https://arxiv.org/abs/quant-ph/0507209"
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