similarity dh-algebras

in  cite{gl}, b. gerla and i. leuc{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, chirtec{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.