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A MODAL TRANSLATION FOR DUAL-INTUITIONISTIC LOGIC

Published online by Cambridge University Press:  12 February 2016

YAROSLAV SHRAMKO
YAROSLAV SHRAMKO*
Affiliation:
Department of Philosophy Kryvyi Rih State Pedagogical University
*
*DEPARTMENT OF PHILOSOPHY KRYVYI RIH STATE PEDAGOGICAL UNIVERSITY KRYVYI RIH, 50086, UKRAINE E-mail: shramko@rocketmail.com
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Abstract

We construct four binary consequence systems axiomatizing entailment relations between formulas of classical, intuitionistic, dual-intuitionistic and modal (S4) logics, respectively. It is shown that the intuitionistic consequence system is embeddable in the modal (S4) one by the usual modal translation prefixing □ to every subformula of the translated formula. An analogous modal translation of dual-intuitionistic formulas then consists of prefixing ◊ to every subformula of the translated formula. The philosophical importance of this result is briefly discussed.

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Type
Research Article
Information
The Review of Symbolic Logic , Volume 9 , Issue 2 , June 2016 , pp. 251 - 265
Copyright
Copyright © Association for Symbolic Logic 2016 

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References

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