A system of fuzzy constructive logic is considered in which the truth values are partially ordered. The notion of algorithmic scale of truth values (shortly, A-scale) is introduced; and on the base of it logical system of generalized fuzzy constructive logic is developed. The classes of identically true predicate formulas in strong and weak sense concerning a given A-scale are introduced. It is proved that any predicate formula of some kind deducible in the constructive (intuitionistic) predicate calculus is identically true in the strong sense concerning any A-scale. From the other side it is proved that some predicate formulas (which are identically true from the classical point of view) are not identically true in the weak sense concerning any A-scale.