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A proof-theoretical investigation of global intuitionistic (fuzzy) logic

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Abstract.

We perform a proof-theoretical investigation of two modal predicate logics: global intuitionistic logic GI and global intuitionistic fuzzy logic GIF. These logics were introduced by Takeuti and Titani to formulate an intuitionistic set theory and an intuitionistic fuzzy set theory together with their metatheories. Here we define analytic Gentzen style calculi for GI and GIF. Among other things, these calculi allows one to prove Herbrand’s theorem for suitable fragments of GI and GIF.

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Authors and Affiliations

  1. Diskrete Mathematik und Geometrie, Research group for Computational Logic, TU, Wien, Austria

    Agata Ciabattoni

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  1. Agata Ciabattoni
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Correspondence to Agata Ciabattoni.

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Work Supported by C. Bühler-Habilitations-Stipendium H191-N04, from the Austrian Science Fund (FWF).

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Ciabattoni, A. A proof-theoretical investigation of global intuitionistic (fuzzy) logic. Arch. Math. Logic 44, 435–457 (2005). https://doi.org/10.1007/s00153-004-0265-8

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