# Axioms or algorithms

Invited Lectures

First Online:

## Abstract

Traditional formal proof systems have been found unusable by those working on such applications of logic as program verification. They demand too much from the proof generator and too little from the proof checker. The notion of proof sketch or informal proof is an unsatisfactory substitute both because it is imprecise and because it treats the symptom rather than the disease. We propose to replace axiomatic proof systems by algorithmic proof systems, which explicitly incorporate a quantitative notion of computational complexity. This proposal depends on the existence of tractable decision procedures for many substantial fragments of logic, the "easy fragments."

## Keywords

Inference Rule Proof System Axiom System Decision Method Tractable Inference
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Preview

Unable to display preview. Download preview PDF.

## Bibliography

- 1.Constable, R.L., On the Theory of Programming Logics, Proc. 9th Ann. ACM Symp. on Theory of Computing, 269–285, Boulder, Col., May 1977.Google Scholar
- 2.Constable, R.L. and M.J. O'Donnell, A Programming Logic, Winthrop Publishers, Inc., 17 Dunster St., Cambridge, Mass., 1978.Google Scholar
- 3.Downey, P., H. Samet, and R. Sethi, Off-line and On-line Algorithms for Deducing Equalities, Conference Record of the Fifth Annual ACM Symposium on Principles of Programming Languages, 158–170, Tucson, Arizona, Jan. 1978.Google Scholar
- 4.Lewis, H., Complexity of Solvable Cases of the Decision Problem for the Predicate Calculus, 19th Annual Symposium on Foundations of Computer Science, Ann Arbor, Michigan, Oct., 1978.Google Scholar
- 5.Litvintchouk, S.D. and V.R. Pratt, A Proof-checker for Dynamic Logic, Proc. 5th Int. Joint Conf. on AI, 552–558, Boston, Aug. 1977.Google Scholar
- 6.Nelson, G. and D.C. Oppen., A Simplifier Based on Efficient Decision Algorithms, Proceedings of the Fifth Annual ACM Symposium on Principles of Programming Languages, 141–150, Tucson, Arizona, Jan. 1978.Google Scholar
- 7.Oppen, D.C., Complexity of Combinations of Quantifier-Free Theories, Proceedings of the Fourth Workshop on Automated Deduction, 67–72, Austin, Texas, Feb. 1979.Google Scholar
- 8.Pratt, V.R., A Near Optimal Method for Reasoning About Action, MIT/LCS/TM-113, M.I.T., Sept. 1978.Google Scholar
- 9.Shostak, R., Deciding Linear Inequalities by Computing Loop Residues, Proceedings of the Fourth Workshop on Automated Deduction, 81–89, Austin, Texas, Feb. 1979.Google Scholar

## Copyright information

© Springer-Verlag Berlin Heidelberg 1979