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

We present a hypersequent calculus ${\text{G}}^3\text{L}\mathrm{\forall }$ for first-order infinite-valued {\L}ukasiewicz logic and for an extension of it, first-order rational Pavelka logic; the calculus is intended for bottom-up proof search. In ${\text{G}}^3\text{L}\mathrm{\forall }$, 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 ${\text{G}}^3\text{L}\mathrm{\forall }$ 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 ${\text{G}}^3\text{L}\mathrm{\forall }$ and thereby provide foundations for proof search algorithms.