Remarks about axiomatizations of certain modal systems.
Bolesław Sobociński · Notre Dame Journal of Formal Logic · 1964
In this paper I present some remarks about axiomatizations of certain modal systems investigated by several authors.Mostly, it will be shown that the axiom-systems of theories under consideration can be simplified.I shall use here a modification of -Lukasiewicz's symbolism in which "C", "K", "A", and "N" possess the ordinary meaning and "M'\ "I,","®" and " §" mean " <>", "~<>~ "> "-}" and "=" respectively.Symbol "f-α " means always: formula a is provable in the system under consideration.If it will be not stated clearly to the contrary, it is always assumed tacitly that a system under consideration has Lewis' primitive terms and rules of procedure.An acquaintance with the modal systems of Lewis is presupposed.The systems often mentioned below, Sl° -S4 G , are defined in [3] and [9], pp.52-53.