# A repetition-free hypersequent calculus for first-order rational Pavelka logic

We present a hypersequent calculus G^3Ł∀ for first-order infinite-valued Łukasiewicz logic and for an extension of it, first-order rational Pavelka logic; the calculus is intended for bottom-up proof search. In G^3Ł∀, there are no structural rules, all the rules are invertible, and designations of multisets of formulas are not repeated in any premise of the rules. The calculus G^3Ł∀ proves any sentence that is provable in at least one of the previously known hypersequent calculi for the given logics. We study proof-theoretic properties of G^3Ł∀ and thereby provide foundations for proof search algorithms.

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