ABSTRACT
For non classical cx , however, the calculi cxqSj are, up to this moment, devoid of any semantical meaning. O f course, the definition of the conse quence operation cs for 2-valued structures im mediately generalizes to that of a consequence operation cs^ for X - valued structures, but the characteri zations of cs in Theorem 1.15.4 and its Corollaries do not work even for cs® [the reason being that a prestructure defined from F m p (L )/R will be a structure only if R is logical, and already in Lemma 1.15.12 the relation S(C ) may not be logical at a ll] . Semantically, however, the connection ct(C) = cs((V ) C) im mediately generalizes to
ctX(C) = cs*((V ) C)
for arbitrary classes X . If cx is at least ce then I can show the
LEMMA 2 If C consists of sentences then cxqtj(C ) = cxqSj(C) .
