Uninorm logic with the n-potency axiom

This paper investigates a class of extensions CnUL of uninorm logic UL, which is obtained by adding the n-potency axiom to UL. The main result of this paper is that by generalizing Jenei and Montagna-style approach for proving standard completeness for monoidal t-norm based logic MTL, we obtain the standard completeness for CnUL. In addition, we present the suitable analytic hypersequent calculi for CnUL.