Involutive uninorm logic with the n-potency axiom

This paper investigates a class of extensions, denoted CnIUL, 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 CnIUL, 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 Jenei's 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.