On axiom systems of propositional calculi, I
Yasuyuki Imai, Kiyoshi Iséki · Proceedings of the Japan Academy Series A Mathematical Sciences · 1965
In a series of our papers, we are mainly concerned with axiom systems of propositional calculi containing many valued propositional calculi and modal logic etc.Our first paper is a preliminary note for our discussions and contains some elementary remarks.In our first some papers, we shall treat two valued propositional calculus.In this series, we shall use the well known symbolisms formulated by J. Lukasiewicz (see 1 and 2), inasmuch as Lukasiewicz symbols are quite helpful and useful for our discussions in axiom systems of propositional calculi.The small Latin letters denote the propositional variables, and the Greek letters denote theses derived from some given axiom system of propositional calculus.The capital Latin letters N and C denote negation and implication respectively.To prove theses of a system of two valued propositional calculus, we use two fundamental rules of inference.