Certification of labeled proofs for modal logics with geometric frame conditions

Abstract : Several proof formalisms have been used, and in some cases even introduced, in order to define proof systems for modal logic. Our work falls within a more general project of establishing a common specification language for checking proofs given in a wide range of deductive formalisms. In this paper, we consider the case of labeled proof systems for modal logics, i.e., in particular, Negri's labeled se-quent calculi, Fitting's prefixed tableaux and free-variable prefixed tableaux, and provide a framework for certifying proofs given in such calculi. The method is based on the use of a translation from the modal language into a first-order polarized language and on a checker whose trusted kernel is a simple implementation of a classical focused sequent calculus. The framework allows for a high flexibility in the representation of proofs to be checked, in the sense that even partial proofs can be verified by employing a process of proof reconstruction. We describe the general method for modal logics characterized by geometric frame conditions, present its implementation in a Prolog-like language, and provide several examples of proof certification in the case of well-known normal modal logics, like K, S4 and S5.
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Contributor : Marco Volpe <>
Submitted on : Tuesday, November 21, 2017 - 10:09:37 AM
Last modification on : Wednesday, March 27, 2019 - 4:41:28 PM

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Tomer Libal, Marco Volpe. Certification of labeled proofs for modal logics with geometric frame conditions. 2017. ⟨hal-01643120⟩

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