Abstract The axiomatic theory of pure free logic, free logic without identity or an existence predicate, contains precisely those axioms and rules that ensure that quantifiers are analyzed as classical quantifiers restricted to a domain of existent objects. This is the content of the soundness and and completeness theorem, which we prove first. We then provide a general method to use this proof in order to yield completeness results for arbitrary extensions of pure free logic.
Manfred Kupffer (Wed,) studied this question.