Abstract Heyting’s intuitionistic predicate logic describes very general regularities observed in constructive mathematics. The intended meaning of the logical constants is clarified through Heyting’s proof interpretation. A re-evaluation of proof interpretation and predicate logic leads to the new constructive Basic logic properly contained in intuitionistic logic. We develop logic and interpretation simultaneously by an axiomatic approach. Basic logic appears to be complete. A brief historical overview shows that our insights are not all new.
Ardeshir et al. (Sun,) studied this question.