In this paper

by using Camberra fuzzy distance on fuzzy set

we propose the notions of Camberra-distance

Camberra-similarity degree between two formulas and Camberra-truth degree of one formula in multiple-valued Lukasiewicz logic system

and discuss the properties of Camberra-similarity degree and Camberra-truth degree

prove that the Camberra-truth degree of formula

φ

is equal to the sum of Camberra-truth degrees of some incompatible formulas. And then

based on Camberra-truth degree

we study some properties of Lukasiewicz logic metric space

prove that there is no isolated point

and arbitrarily sphere neighbourhood is an inconsistent theory in three valued L

ukasiewicz logic metric space and so on. Which provides a new method for expand the grade reasoning on formula set

F

(

S

).