An axiomatization for until and since over the reals without the IRR rule (Q1207338)

This paper deals with different kinds of approaches to axiomatization of temporal logic. The author considers the case of temporal logic with two temporal connectives: ``until'' and ``since''. The considered semantics consists of linear temporal structures with irreflexive linear order (flow of time). The offered axiomatic system for this temporal logic of real flow of time consists of some Burgess-Xu axioms, axioms of density and no end points, and some additional ones. A similar axiomatic system for ``until''-``since'' temporal logic of integers is also given. These axiomatic systems are orthodox (have only usual temporal rules).