Abstract
We present a sequent calculus for the Grzegorczyk modal logic Grz allowing cyclic and other non-well-founded proofs and obtain the cut-elimination theorem for it by constructing a continuous cut-elimination mapping acting on these proofs. As an application, we establish the Lyndon interpolation property for the logic Grz proof-theoretically.
Original language | English |
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Pages (from-to) | 22-50 |
Journal | The Review of Symbolic logic |
Volume | 14 |
Issue number | 1 |
DOIs | |
Publication status | Published - 29 Jun 2020 |
Externally published | Yes |
Keywords
- non-well-founded proofs
- Grzegorczyk logic
- cut-elimination
- Lyndon interpolation
- cyclic proofs