A refinement of the concept of an axiomatic system

Abstract

The aim of this paper is to propose a particular conception and formulation of the concepts of formal derivation and axiomatic system, which, although not orthodox, remain part of classical first order logic. It is proposed, in particular, that the definition of formal derivation includes the possibility of establishing restrictions to the applications of inference rules and that this improved definition be subsumed as a part of the very notion of axiomatic system. This syntactic notion of formal derivation in formal systems is more adequate to classical semantic logical consequence.