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

We present a hypersequent calculus \text{G}^3\text{\L}\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}\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}\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}\forall and thereby provide foundations for proof search algorithms.Comment: 21 pages; corrected a misprint, added an appendix containing errata to a cited articl