Monadic k x j-rough Heyting algebras

Abstract

In this paper, we introduce the variety of algebras, which we call monadic kxj-rough Heyting algebras. These algebras constitute an extension of monadic Heyting algebras and in 3x2 case they coincide with monadic 3-valued Lukasiewicz--Moisil algebras. Our main interest is the characterization of simple and subdirectly irreducible monadic kxj-rough Heyting algebras. In order to this, an Esakia-style duality for these algebras is developed.