5 papers · 1 filter
Proof Theory and Interpolation for Sacchetti's Logics
Borja Sierra Miranda, Thomas Studer
We study the proof theory of Sacchetti's modal logics, a family of logics generalizing Gödel--Löb provability logic by replacing transitivity with n-transitivity. We make three m…
Proof Theory for Bimodal Provability Logics
Borja Sierra Miranda, Thomas Studer
We provide the first (non-labelled) sequent calculi for bimodal provability logics with "usual" provability predicates. In particular, we introduce calculi for the logics CS, CSM a…
Uniform interpolation for interpretability logic
Sebastijan Horvat, Borja Sierra Miranda, Thomas Studer
We present a proof-theoretical study of the interpretability logic IL, providing a wellfounded and a non-wellfounded sequent calculus for IL. The non-wellfounded calculus is used t…
Cut elimination for a non-wellfounded system for the master modality
Borja Sierra Miranda, Thomas Studer
In previous work we provided a method for eliminating cuts in non-wellfounded proofs with a local-progress condition, these being the simplest kind of non-wellfounded proofs. The m…
Coalgebraic proof translations for non-wellfounded proofs
Borja Sierra Miranda, Thomas Studer, Lukas Zenger
Non-wellfounded proof theory results from allowing proofs of infinite height in proof theory. To guarantee that there is no vicious infinite reasoning, it is usual to add a constra…