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',V and A on L by these operations such that if these operations satisfy t...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',V and A on L by these operations such that if these operations satisfy the seven axioms of lattice implication algebra then(L,V.∧,’)is a com plemented 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 with.out any algebraic structure.展开更多
基金Supported by the National Natural Science Foundation of China(60074014)
文摘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',V and A on L by these operations such that if these operations satisfy the seven axioms of lattice implication algebra then(L,V.∧,’)is a com plemented 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 with.out any algebraic structure.
