Similarity DH-Algebras

In \cite{GL}, B. Gerla and I. Leu\c{s}tean introduced the notion of similarity on MV-algebra. A similarity MV-algebra is an MV-algebra endowed with a binary operation S that verifies certain additional properties. Also, Chirte\c{s} in \cite{C}, study the notion of similarity on \L ukasiewicz-Moisil algebras. In particular, strong similarity \L ukasiewicz-Moisil algebras were defined. In this paper we define and study the variety of similarity symmetric Heyting algebras (or similarity DH-algebras), i.e. symmetric Heyting algebras endowed with an operation of similarity S. These algebras are a generalization of strong similarity \L ukasiewicz-Moisil algebras. In addition, we introduce a propositional calculus and prove this calculus has similarity DH-algebras as algebraic counterpart.