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A theorem prover and countermodel constructor for provability logic in HOL Light
[article]

2022
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arXiv
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pre-print

We introduce our implementation in HOL Light of a prototype of a general theorem prover for normal modal logics. In the present work, we start by considering G\"odel-L\"ob provability logic (GL). The methodology consists of a shallow embedding of a labelled sequent calculus for GL whose validity relies on our formalised proof in HOL Light of modal completeness for GL w.r.t. possible world semantics, that we present in the first part of the present work. Our theorem prover for GL is thus

arXiv:2205.03659v1
fatcat:5ik6aviqlfgafb5rwkh75bhsu4