Uninorm logic with the -potency axiom

This paper investigates a class of extensions C n UL 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 C n UL . In addition, we present the suitable analytic hypersequent calculi for C n UL .