A MODAL TRANSLATION FOR DUAL-INTUITIONISTIC LOGIC. Issue 2 (12th February 2016) - SHRAMKO, YAROSLAV
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.