The construction of a logic metric space is studied in detail. It is proved that there exists a reflexive transformation φ on a classical logic metric space. The transformation φ is a homomorphic mapping and keeps the logic equivalence relation unchanged. And φ naturally induces a reflexive transformation φ* on the Lindenbaum algebra, which is an automorphic and isometric transformation of the Lindenbaum algebra. Moreover, the general forms of fixed points have been obtained by studying the features of fixed points (such as [A]∨φ*([A]) or [A]∧φ*([A]),A∈F(S)). Lastly, the above mentioned interesting properties do not hold for the n-valued Gdel type logic metric space whenever n>2.

classical logic; Lindenbaum algebra; logic metric space; reflexive transformation; automorphism; fixed point; n-valued Gdel type logic metric space