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A MODAL TRANSLATION FOR DUAL-INTUITIONISTIC LOGIC.

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 transla...

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Published in:Review of Symbolic Logic Vol. 9; no. 2; pp. 251 - 266
Main Author: SHRAMKO, YAROSLAV
Format: Article
Published: Cambridge University Press Jun2016
Subjects:
Intuitionistic mathematics
Mathematical logic
Binary number system
Computer arithmetic
Mathematical formulas
Online Access:View this record in EBSCOhost
Summary: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.