Abstract
In this paper we treat metasequents—objects which stand to sequents as sequents stand to formulas—as first class logical citizens. To this end we provide a metasequent calculus, a sequent calculus which allows us to directly manipulate metasequents. We show that the various metasequent calculi we consider are sound and complete w.r.t. appropriate classes of tetravaluations where validity is understood locally. Finally we use our metasequent calculus to give direct syntactic proofs of various collapse results, closing a problem left open in French (Ergo, 3(5), 113–131 2016).
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Acknowledgements
I would like to thank audiences at the VI Workshop on Philosophical Logic at the University of Buenos Aires, the Melbourne Logic Group, the Berkeley Logic Colloquium, and the Logic & Philosophy special session at the 2021 Pacific APA. Special thanks are also due to David Ripley, Shawn Standefer, and two anonymous referees for this journal for their helpful comments, and to Eduardo Barrio and Paul Egré for their patience and understanding.
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French, R. Metasequents and Tetravaluations. J Philos Logic 51, 1453–1476 (2022). https://doi.org/10.1007/s10992-021-09623-7
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DOI: https://doi.org/10.1007/s10992-021-09623-7