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About this paper
Iris van der Giessen, Raheleh Jalali, Roman Kuznets
This chapter from a forthcoming book offers a comprehensive overview of proof-theoretic methods for deriving interpolation properties in various logical systems. It details constructive approaches for extracting interpolants, such as Maehara's and Pitts' methods, and extends these to modern formalisms like labelled and hypersequents, linking them to universal proof theory for logic classification.
Key insights
- Proof-theoretic methods provide constructive and algorithmic approaches for extracting interpolants directly from (or via search in) proofs.
- Interpolation properties serve as crucial logical invariants that dictate the feasibility of constructing "well-behaved" sequent calculi for various logics.
- Generalized sequent calculi like labelled, hyper-, and nested sequents are effective for applying interpolation methods to logics where traditional calculi are insufficient.
Summary by alphaXiv.
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