Involutive uninorm logic with the n-potency axiom

This paper investigates a class of extensions, denoted C n IUL , of the involutive uninorm logic IUL , which is obtained by adding the n-potency axiom to IUL . The main result of this paper is the proof of the standard completeness for C n IUL , which is obtained by generalizing Jenei and Montagna-style approach for proving standard completeness for MTL . In addition, this result also presents a generalization of Jeneiʹs embedding method of constructing left-continuous t-norms, which can generate a countable number of left-continuous and involutive conjunctive uninorms and provides a tremendously wide spectrum of choice for e.g. logical and set theoretical connectives in non-classical logic and in fuzzy theory.