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This study generalizes a parameterized interpolation system for propositional resolution proofs to hyper-resolution and clausal proofs. This enhanced system offers greater flexibility in generating interpolants, improving automated reasoning and model checking.

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Area of Science:

  • Automated reasoning
  • Formal verification
  • Mathematical logic

Background:

  • Craig's interpolation theorem is crucial for model checking, automated reasoning, and synthesis.
  • Existing interpolation systems are often rigid, providing only one interpolant per proof.
  • Previous work introduced a parameterized system for propositional resolution, allowing variable and strength variation.

Purpose of the Study:

  • To generalize the parameterized interpolation system to propositional hyper-resolution and clausal proofs.
  • To extend the flexibility of interpolant generation beyond existing rigid systems.
  • To analyze the relationship between the generalized system and first-order logic interpolation.

Main Methods:

  • Generalization of a parameterized interpolation system.
  • Application to propositional hyper-resolution proofs.
  • Application to clausal proofs generated by SAT solvers.
  • Analysis of interpolants derived from local (split) proofs.

Main Results:

  • The generalized system accommodates propositional hyper-resolution and clausal proofs.
  • The system allows systematic variation of logical strength and elimination of non-essential variables.
  • When applied to local proofs, the extension unifies two first-order logic interpolation systems.

Conclusions:

  • The generalized interpolation system offers a more flexible and systematic approach to interpolant generation.
  • This work bridges propositional and first-order logic interpolation methods.
  • The findings have implications for improving automated reasoning and verification tools.