Model-Theoretic Investigations into Consequence Operation (Cn) in Quantum Logics. An Algebraic Approach

Details Model-Theoretic Investigations into Consequence Operation (Cn) in Quantum Logics. An Algebraic Approach Model-Theoretic Investigations into Consequence Operation (Cn) in Quantum Logics. An Algebraic Approach

2005-07-21

arxiv.org/abs/quant-ph/0507209v2

International Journal of Theoretical Physics, 45, No. 4, 695-705 (2006)

Physics

Quantum Physics

11 pages

Scientific paper

10.1007/s10773-006-9060-0

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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