Abstract
Hypersequents are a natural generalization of ordinary sequents which turn out to be a very suitable tool for presenting cut-free Gentzent-type formulations for diverse logics. In this paper, an alternative way of formulating hypersequent calculi (by introducing meta-variables for formulas, sequents and hypersequents in the object language) is presented. A suitable category of hypersequent calculi with their morphisms is defined and both types of fibring (constrained and unconstrained) are introduced. The introduced morphisms induce a novel notion of translation between logics which preserves metaproperties in a strong sense. Finally, some preservation features are explored.
This paper constitutes a revised, extended and improved version from the preprint [9]. That preliminary version is described with full details in [10].
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Acknowledgements
The first author was financed by FAPESP (Brazil), Thematic Project LogCons (2010/51038-0), as well as by an individual research grant from The National Council for Scientific and Technological Development (CNPq), Brazil. The second author wants to acknowledge the hospitality of CLE (UNICAMP, Brazil), where the writing of this paper was begun. Also, he wants to thank the National University of the South—UNS (Bahía Blanca, Argentina) for supporting his stay at Campinas, Brazil.
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Dedicated to Jean-Yves Béziau on the occasion of his 50th birthday.
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Coniglio, M.E., Figallo, M. (2015). A Formal Framework for Hypersequent Calculi and Their Fibring. In: Koslow, A., Buchsbaum, A. (eds) The Road to Universal Logic. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-10193-4_4
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DOI: https://doi.org/10.1007/978-3-319-10193-4_4
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