Comparing several calculi for first-order infinite-valued Łukasiewicz logic

12/13/2018

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by   Alexander S. Gerasimov, et al.

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From the viewpoint of provability, we compare some Gentzen-type hypersequent calculi for first-order infinite-valued Łukasiewicz logic and for first-order rational Pavelka logic with each other and with Hájek's Hilbert-type calculi for these logics. The key aspect of our comparison is a density elimination proof for one of the hypersequent calculi considered.