A Method for Constructing Lattice Implication Algebras on the Interval [0,1]
Xuefang Wang, Peishun Liu · 2008
The uniqueness of LIA-implication on some Kleene algebra is investigated and a method for constructing new lattice implication algebra on Kleene algebra is given. By this method we construct at least countable many lattice implication algebras on the real unit interval [0,1] which are different from Lukasiewicz implication algebra. This shows that Lukasiewicz implication algebra is not the unique lattice implication algebra on [0,1].