Representation theorems for some fuzzy logics based on residuated non-distributive lattices

In this paper we present the representation theorems for three classes of algebras based on residuated, not necessarily distributive lattices. These structures are algebras of weak fuzzy logics, which are the bottom part of the hierarchy of fuzzy logics proposed by Esteva and Godo. Our results are based on the methodology proposed by Urquhart and Allwein and Dunn. The representation algebras provide a Kripke–style semantics for the respective fuzzy logics.