Imagen de Portada
Código QR

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...

Descripción completa

Publicado en:Review of Symbolic Logic Vol. 9; no. 2; pp. 251 - 266
Autor principal: SHRAMKO, YAROSLAV
Formato: Artículo
Publicado: Cambridge University Press Jun2016
Materias:
Intuitionistic mathematics
Mathematical logic
Binary number system
Computer arithmetic
Mathematical formulas
Acceso en línea:Ver este registro en EBSCOhost
Sumario: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.