A Note on the Axioms of Lattice Implication Algebra
Zhao Guang · Shuxue jikan · 2002
This paper proved that when we have a binary operation and two nullary operations O and I on a non_empty set L, we can define the operations′, ∨ and ∧ on L by these operations such that if these operations satisfy the seven axioms of lattice implication algebra then (L,∨,∧,′) is a complemented lattice with universal bounds. So, when we define lattice implication algebra, we needn't start on a complemented lattice with universal bounds, but we can begin with a non_empty set without any algebraic structure.