Axiomatizations of Temporal Logic . 10723029 Xu Zhaoqing. I. Content. Introduction Basic temporal logic Branching time logic Conclusions. II. Introduction. Temporal Logic Broadly : all approaches to the representation of temporal information within a logical framework;
Fϕ =df ¬G¬ϕ
Pϕ =df ¬H¬ϕ
Atemporal frame (or flow of time) F=(T,＜)，where T is non-empty，＜is a binary relation which is irreflexive and transitive;
A valuation V:Ф→P(T); A model M=(F,V);
F≤ϕ =df ϕ∨Fϕ，G≤ϕ =df ϕ∧Gϕ，P≤ϕ =df ϕ∨Pϕ，H≤ϕ =df ϕ∧Hϕ.
(fϕ)o = □Fϕo and (Gϕ)o = □Gϕo
M, t||- ϕ iff M,t, b||- ϕo
We’ve known that every strongly valid Ockhamist formula is valid, but the converse is not right.
 Y. Gurevich and S. Shelah. The decision problem for branching time logic. In The Journal of Symbolic Logic, 50, 668-681,1985.
 M. Reynolds,An Axiomatization of Prior’s Ockhmist Logic of Historical Necessity，to appear.
 Y. Venema, Temporal Logic, in The Blackwell Guide to Philosophical Logic, Blackwell publishers, 2001.