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The deduction theorem for quantum logic—some negative results

Published online by Cambridge University Press:  12 March 2014

Jacek Malinowski
Jacek Malinowski*
Affiliation:
Section of Logic, Institute of Philosophy And Sociology, Polish Academy of Sciences, 90-365 Łódź, Poland
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Abstract

We prove that no logic (i.e. consequence operation) determined by any class of orthomodular lattices admits the deduction theorem (Theorem 2.7). We extend those results to some broader class of logics determined by ortholattices (Corollary 2.6).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 55 , Issue 2 , June 1990 , pp. 615 - 625
Copyright
Copyright © Association for Symbolic Logic 1990

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References

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