On Monadic Semi-Nelson Algebras

In this paper, we equip the variety of semi-Nelson algebras with universal and existential quantifiers and introduce monadic semi-Nelson algebras. The monadic N-deductive systems and monadic congruences of monadic semi-Nelson algebras are defined and their properties are studied. We prove a one-to-one correspondence exists between the set of monadic congruences and the set of monadic N-deductive systems. The monadic semi-intuitionistic logic with strong negation is constructed. Based on the monadic semi-Nelson algebras, we prove the completeness and soundness of The monadic semi-intuitionistic logic with strong negation. © 2024, College Publications. All rights reserved.