Embedding deduction modulo into a prover

Authors:
Guillaume Burel
Affiliations:
Max Planck Institute for Informatics, Saarland University, Saarbrücken, Germany
Venue:
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Year:
2010

Citing 11
Cited 1

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

Journal of the ACM (JACM)
Resolution Strategies as Decision Procedures

Journal of the ACM (JACM)
What Is a Theory?

STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Proof Normalization for Resolution and Paramodulation

RTA '89 Proceedings of the 3rd International Conference on Rewriting Techniques and Applications
Theorem Proving Modulo

Journal of Automated Reasoning
HOL-λσ: an intentional first-order expression of higher-order logic

Mathematical Structures in Computer Science
How can we prove that a proof search method is not an instance of another?

Proceedings of the Fourth International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice
Progress in the Development of Automated Theorem Proving for Higher-Order Logic

CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Resolution is Cut-Free

Journal of Automated Reasoning
Truth values algebras and proof normalization

TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
Arithmetic as a theory modulo

RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications

Experimenting with deduction modulo

CADE'11 Proceedings of the 23rd international conference on Automated deduction

Quantified Score

Hi-index	0.00

Visualization

Abstract

Deduction modulo consists in presenting a theory through rewrite rules to support automatic and interactive proof search. It induces proof search methods based on narrowing, such as the polarized resolution modulo. We show how to combine this method with more traditional ordering restrictions. Interestingly, no compatibility between the rewriting and the ordering is requested to ensure completeness. We also show that some simplification rules, such as strict subsumption eliminations and demodulations, preserve completeness. For this purpose, we use a new framework based on a proof ordering. These results show that polarized resolution modulo can be integrated into existing provers, where these restrictions and simplifications are present. We also discuss how this integration can actually be done by diverting the main algorithm of state-of-the-art provers.