A Calculational Deductive System for Linear Temporal Logic
Department(s)
Natural Science
Document Type
Article
Publication Date
6-1-2020
Keywords
Calculational logic, equational logic, linear temporal logic
Abstract
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.
Publication Title
ACM Computing Surveys
ISSN
03600300
E-ISSN
15577341
Volume
53
Issue
3
DOI
10.1145/3387109
Recommended Citation
Warford, J. Stanley; Vega, David; and Staley, Scott M., "A Calculational Deductive System for Linear Temporal Logic" (2020). Pepperdine University, All Faculty Open Access Publications. Paper 41.
https://digitalcommons.pepperdine.edu/faculty_pubs/41