Similarity operations on equality algebras

In this paper, we apply the concept of similarity operations to equality algebras and introduce similarity equality algebras. We investigate some related properties of them. In particular, we prove that there is a one to one correspondence between similarity filters and similarity congruence relations on a similarity equality algebra. Furthermore, we prove the first isomorphism theorem on similarity equality algebras. We use the similarity filters to establish the uniform structure on similarity equality algebras and obtain some properties of this topology. In addition, we introduce and study a corresponding propositional logic for similarity equality algebras and prove the soundness and completeness of this propositional logic based on similarity equality algebras.