Experiment with an automatic theorem-prover having partial ordering inference rules

Authors:
James R. Slagle;Lewis M. Norton
Affiliations:
National Institutes of Health, Bethesda, MD;National Institutes of Health, Bethesda, MD
Venue:
Communications of the ACM
Year:
1973

Citing 4
Cited 10

Efficiency and Completeness of the Set of Support Strategy in Theorem Proving

Journal of the ACM (JACM)
Two Results on Ordering for Resolution with Merging and Linear Format

Journal of the ACM (JACM)
Automatic Theorem Proving with Built-in Theories Including Equality, Partial Ordering, and Sets

Journal of the ACM (JACM)
Proof of a program: FIND

Communications of the ACM

Some Inference Rules for Integer Arithmetic for Verification of Flowchart Programs on Integers

IEEE Transactions on Software Engineering
A Theorem Prover for Verifying Iterative Programs Over Integers

IEEE Transactions on Software Engineering
A Set of Inference Rules for Quantified Formula Handling and Array Handling in Verification of Programs Over Integers

IEEE Transactions on Software Engineering
Proving refutational completeness of theorem-proving strategies: the transfinite semantic tree method

Journal of the ACM (JACM)
Automated Theorem-Proving for Theories with Simplifiers Commutativity, and Associativity

Journal of the ACM (JACM)
A program verification system

ACM '76 Proceedings of the 1976 annual conference
The roots of structured programming

SIGCSE '78 Papers of the SIGCSE/CSA technical symposium on Computer science education
The NIH Heuristics laboratory

ACM SIGART Bulletin
The Use of Higher Order Logic in Program Verification

IEEE Transactions on Computers
Complete inference rules for the cancellation laws

IJCAI'87 Proceedings of the 10th international joint conference on Artificial intelligence - Volume 2

Quantified Score

Hi-index	48.22

Visualization

Abstract

Automatic theorem-provers need to be made much more efficient. With this in mind, Slagle has shown how the axioms for partial ordering can be replaced by built-in inference rules when using a particular theorem-proving algorithm based upon hyper-resolution and paramodulation. The new rules embody the transitivity of partial orderings and the close relationship between the ⊂ and ⊆ predicates. A program has been developed using a modified version of these rules. This new theorem-prover has been found to be very powerful for solving problems involving partial orderings. This paper presents a detailed description of the program and a comprehensive account of the experiments that have been performed with it.