We consider first-order infinite-valued Łukasiewicz logic and its expansion, rational Pavelka RPL∀. From the viewpoint of provability, we compare several Gentzen-type hypersequent calculi for these logics with each other Hájek’s Hilbert-type same logics. To facilitate comparing previously known logics, define two new analytic RPL∀ include them in our comparison. The key part comparison is a den...

We define a procedure for translating given first-order formula to an equivalent modal formula, if one exists, by using tableau-based bisimulation invariance test. A previously developed tableau tests of and therefore whether that is the standard translation some formula. Using closed as starting point, we show how can be effectively obtained.