Problem
Research questions and friction points this paper is trying to address.
uniform Lyndon interpolation
provability logic
GLS
non-wellfounded proofs
Uniform Lyndon Interpolation via Non-wellfounded Proofs
🤖 AI Summary
This study resolves the long-standing open question of whether the provability logic GLS enjoys the uniform Lyndon interpolation property. By introducing a non-well-founded sequent calculus, we simultaneously establish both uniformity and the Lyndon property for interpolants, thereby providing a novel proof of cut elimination for GLS. Our approach not only confirms that GLS possesses the uniform Lyndon interpolation property but also constructs a general framework amenable to extension to other provability logics, demonstrating its potential for broader applicability across related systems.
📝 Abstract
Non-wellfounded proof theory has been applied to establish uniform interpolation and Lyndon interpolation (separately) for multiple logics. However, it has not yet been used to prove uniform Lyndon interpolation. We close this gap by showing uniform Lyndon interpolation for the provability logic GLS. This logic was known to have uniform interpolation, but it was open whether it has uniform Lyndon interpolation (or at least non-uniform Lyndon interpolation). The methodology we provide is easy to adapt to other provability logics if a non-wellfounded sequent calculus is available for them. In addition, we offer an alternative proof of cut elimination for GLS via non-wellfounded proofs.
Innovation
Methods, ideas, or system contributions that make the work stand out.
uniform Lyndon interpolation
non-wellfounded proofs
provability logic GLS
cut elimination
sequent calculus
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