A Calculational Deductive System for Linear Temporal Logic

This article surveys the linear temporal logic (LTL) literature and presents all the LTL theorems from the survey, plus many new ones, in a calculational deductive system. Calculational deductive systems, developed by Dijkstra and Scholten and extended by Gries and Schneider, are based on only four inference rules—Substitution, Leibniz, Equanimity, and Transitivity. Inference rules in the older Hilbert-style systems, notably modus ponens, appear as theorems in this calculational deductive system. This article extends the calculational deductive system of Gries and Schneider to LTL, using only the same four inference rules. Although space limitations preclude giving a proof of every theorem in this article, every theorem has been proved with calculational logic.