Nota sobre el significado lógico de ciertas estructuras residuadas elementales

Abstract

Starting from an abelian grupoid which is ordered and residuated we study the logical significance of the 'residue' operation, specially if we add the most natural algebraic properties to the base structure, obtaining then several well-Known structures of mathematical logic, such as the deductively-complete algebras and the algebras of Sales,Hilbert,Abbott,Wajsberg and Boole .We also give some properties of the deductive systems and obtain an special version of the deduction theorem of Pla( [3] ) .