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A Comprehensive Framework for Saturation Theorem Proving
Uwe Waldmann1, Sophie Tourret1,2, Simon Robillard3
1Max-Planck-Institut für Informatik, Saarland Informatics Campus, Saarbrücken, Germany.
Journal of Automated Reasoning
|November 10, 2022
Summary
This study formalizes redundancy criteria for saturation theorem provers, ensuring deleted formulas are truly redundant. This framework guarantees dynamic refutational completeness for automated theorem provers.
Area of Science:
- Automated Theorem Proving
- Formal Methods
- Logic
Background:
- Saturation theorem provers rely on deleting subsumed formulas for efficiency.
- Existing formalizations of redundancy and completeness are often informal or cumbersome.
- Standard redundancy definitions are insufficient for complex theorem proving scenarios.
Purpose of the Study:
- To present a formal framework for proving refutational completeness of abstract saturation provers.
- To extend redundancy criteria to formally handle subsumption.
- To model prover architectures for guaranteed dynamic refutational completeness.
Main Methods:
- Development of a framework for formal refutational completeness proofs.
- Modular extension of redundancy criteria using ground-to-nonground lifting.
- Mechanization of the framework in Isabelle/HOL.
Main Results:
- A formal method to ensure deleted formulas are redundant, strengthening completeness proofs.
- Extended redundancy criteria that effectively incorporate subsumption.
- A framework that bridges static calculus completeness with dynamic prover completeness.
Conclusions:
- The proposed framework provides a rigorous approach to automated theorem prover completeness.
- Formalizing redundancy criteria enhances the reliability and efficiency of saturation provers.
- The mechanization in Isabelle/HOL validates the framework's practical applicability.
Keywords:
Automated theorem provingProver architecturesRedundancyResolution calculusSaturationSuperposition calculusMore Related Videos
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