Logics for residuated pseudo-uninorms and their residua

With the aim of capturing the logic of residuated pseudo-uninorms and their residua, we introduce an axiomatic extension of the system of bounded representable residuated lattices of Metcalfe, Olivetti and Gabbay. Since many known non-commutative fuzzy logics are axiomatic extensions of their system, it plays an important role among non-commutative fuzzy logics. By adding the so-called n-potency axiom to our system, we prove that standard completeness can be obtained. This result supports our conjecture that our system is the logic of residuated pseudo-uninorms and their residua.