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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.

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|November 10, 2022
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Summary
This summary is machine-generated.

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.

Keywords:
Automated theorem provingProver architecturesRedundancyResolution calculusSaturationSuperposition calculus

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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.