Approximate Completeness of Hypersequent Calculus for First-Order ukasiewicz Logic
Abstract
Hypersequent calculus G∀ for first-order ukasiewicz logic was first introduced by Baaz and Metcalfe, along with a proof of its approximate completeness with respect to standard [0,1]-semantics. The completeness result was later pointed out by Gerasimov that it only applies to prenex formulas. In this paper, we will present our proof of approximate completeness of G∀ for arbitrary first-order formulas by generalizing the original completeness proof to hypersequents.
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