Comparing Calculi for First-Order Infinite-Valued Łukasiewicz Logic and First-Order Rational Pavelka Logic
DOI:
https://doi.org/10.12775/LLP.2022.030Keywords
many-valued logic, mathematical fuzzy logic, first-order infinite-valued Lukasiewicz logic, first-order rational Pavelka logic, proof theory, Hilbert-type calculus, Gentzen-type hypersequent calculus, density elimination, conservative extensionAbstract
We consider first-order infinite-valued Łukasiewicz logic and its expansion, first-order rational Pavelka logic RPL∀. From the viewpoint of provability, we compare several Gentzen-type hypersequent calculi for these logics with each other and with Hájek’s Hilbert-type calculi for the same logics. To facilitate comparing previously known calculi for the logics, we define two new analytic calculi for RPL∀ and include them in our comparison. The key part of the comparison is a density elimination proof that introduces no cuts for one of the hypersequent calculi considered.
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