The Equivalent Definitions of Lattice Implication Algebra

Abstract

This paper proved that when we have a binary operation rightarrow and a nullary operations rarr on a non-empty set L, if these operations satisfy the four axioms of lattice implication algebra, then (L, rarr, 0) will be a lattice implication algebra. So, when we define lattice implication algebra, we needn't start on a complemented lattice with universal bounds, but we can begin with an algebra of type (2,0).