Introducció d'interiors d'ordre en lògiques abstractes

Abstract

Let L = (S,C) be an abstract logic ( El]) . Using the methods of 131 we study the abstract logic . Lo = (S,C0) agsociated with 11,=1X C- S :X=C(X), f (XXX } for a given mapping f: S > S . We see that Lo preserves several logical properties of L . We state necessary and sufficient conditions on C to obtain separately the three properties of an interior mapping on the logical quotient of S by C, when the last is an ordered set, a semilattice, or an implicative algebra.