Some Remarks on Lattice Implication Algebra

A sufficient and necessary consition for a general (2,1,0,0) type algebra (L,→,*,0,1) to be a lattice implication algebra is presented. It is proved that in a finite chain and in a non-linear four-element lattice there exists only one lattice implication algebra, but no implication algebra in a non-linear five-element lattice. This provides the foundation for further study of the structure of lattice implication algebra that is composed of linguistic true values.