On the Proof-Theory of two Formalisations of Modal First-Order Logic |
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Authors: | Yehuda Schwartz George Tourlakis |
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Institution: | 1.Mathematics and Statistics,York University,Toronto,Canada;2.Computer Science & Engineering, Mathematics and Statistics,York University,Toronto,Canada |
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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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