Abstract
We introduce a Gentzen-style modal predicate logic and prove the cut-elimination theorem for it. This sequent calculus of cut-free proofs is chosen as a proxy to develop the proof-theory of the logics introduced in [14, 15, 4]. We present syntactic proofs for all the metatheoretical results that were proved model-theoretically in loc. cit. and moreover prove that the form of weak reflection proved in these papers is as strong as possible.
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Schwartz, Y., Tourlakis, G. On the Proof-Theory of two Formalisations of Modal First-Order Logic. Stud Logica 96, 349–373 (2010). https://doi.org/10.1007/s11225-010-9294-y
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DOI: https://doi.org/10.1007/s11225-010-9294-y