for n dimensional truth value functions constituting the double lattice ordered semigroup

The thesis gives that n_dimensional truth_value functional set is a F_lattice semigroup concerning as follows the operation ∨ and the dual operation ∧,and the ordering relation ≤ constituting the boolean algebra:f∨g(x)=f(x)∨g(x),f∧g(x)=f(x)∧g(x) (f,g∈L,x∈｛0,1｝n),f≤g is and only is f(x)≤g(x)(f,g∈L,x∈｛0,1｝n). And its molecule structure make sured. The thesis point out to the quotient structure M/ and L are isomorphic,M means for Proposition formulas to contain n Proposition Variable constituting the set and means the equal relation of Proposition formulas,accordingly showed the cadre of the Propositional logic is a special double lattice_ordered semigroup, i.e.F lattice_ordered semigroup. 