Temporal Logic of Programs

Logic and Programs.- Historical Remarks.- Some Concepts and Notions of Classical Logic.- I. Propositional Temporal Logic.- 1. A Language TTA of Propositional Temporal Logic.- 2. Semantics of TTA.- 3. Temporal Logical Laws.- 4. Some Further Temporal Operators.- II. Axiomatization of Propositional Temporal Logic.- 5. The Formal System ?TA.- 6. Completeness of ?TA.- 7. Induction Principles.- III. First-Order Temporal Logic.- 8. First-Order Temporal Languages and Their Semantics.- 9. The Formal System ?TP.- 10. The Principle of Well-Founded Orderings.- 11. Additional Propositional Variables.- IV. Temporal Semantics of Programs.- 12. Programs.- 13. Execution Sequences of Programs.- 14. Program Axioms.- 15. Description of Program Properties.- V. Invariance and Precedence Properties of Programs.- 16. The Basic Invariant Method.- 17. Examples of Applications.- 18. Invariant Methods for Precedence Properties.- 19. Examples of Applications.- VI. Eventuality Properties of Programs.- 20. Fair Execution Sequences.- 21. The Finite Chain Reasoning Method.- 22. The Method of Well-Founded Orderings.- 23. Examples of Applications.- VII. Special Methods for Sequential Programs.- 24. Hoare’s Calculus.- 25. The Intermittent Assertion Method.- 26. Examples of Applications.- Bibliographical Remarks.- Appendix: Table of Laws and Rules.- References.