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.
CITATION STYLE
Coniglio, M. E., & Figallo, M. (2015). A Formal Framework for Hypersequent Calculi and Their Fibring. In Studies in Universal Logic (pp. 73–93). Springer Nature. https://doi.org/10.1007/978-3-319-10193-4_4
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