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A general proof certification framework for modal logic

Published online by Cambridge University Press:  26 March 2019

TOMER LIBAL  and
MARCO VOLPE
TOMER LIBAL
Affiliation:
The American University of Paris, Paris, France Email: tlibal@aup.edu
MARCO VOLPE
Affiliation:
Fortiss GmbH, Munich, Germany Email: volpe@fortiss.org
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Abstract

One of the main issues in proof certification is that different theorem provers, even when designed for the same logic, tend to use different proof formalisms and produce outputs in different formats. The project ProofCert promotes the usage of a common specification language and of a small and trusted kernel in order to check proofs coming from different sources and for different logics. By relying on that idea and by using a classical focused sequent calculus as a kernel, we propose here a general framework for checking modal proofs. We present the implementation of the framework in a Prolog-like language and show how it is possible to specialize it in a simple and modular way in order to cover different proof formalisms, such as labelled systems, tableaux, sequent calculi and nested sequent calculi. We illustrate the method for the logic K by providing several examples and discuss how to further extend the approach.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 29 , Special Issue 8: A special issue on structural proof theory, automated reasoning and computation in celebration of Dale Miller’s 60th birthday , September 2019 , pp. 1344 - 1378
Copyright
© Cambridge University Press 2019 

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