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Symposium on logic and computability "Logic and Computation Day"
June 7, 2013 12:15–13:00, Moscow, Steklov Mathematical Institute of RAS
 


Circular proofs for provability logic

D. S. Shamkanov

Steklov Mathematical Institute of the Russian Academy of Sciences

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Abstract: We present a circular proof system for the Gödel-Löb provability logic GL. In contrast to the ordinary proofs, a circular proof can be formed from an ordinary derivation tree by identifying each open assumption with an identical interior sequent. We prove that the circular proof-system is sound and complete with respect to the standard sequent-style formulation of GL, that it is contraction-free and cut-free, and that its logical rules are invertible. As an application, we give a syntactic proof of Lyndon interpolation for GL.

Language: English

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