The notion of Choquet integral truth degrees of propositions in Lukasiewicz propositional logic is introduced

by means of the Choquet integral of McNaughton functions with respect to uncertainty measures on the set of all valuations.When the involved uncertainty measures satisfy finite additivity property

the notion of Choquet integral truth degrees can induce in a natural way a pseudo-metric

with which the set of all propositions becomes a pseudo metric space and thus several graded reasoning methods can be established.The notion of Choquet integral truth degrees will reduce to the existing notion of Borel probability truth degrees in probabilistically quantitative logic when the uncertainty measures are Borel probability measures.This paper is a continuation of probabilistically quantitative logic and provides a possible framework for reasoning about non-linear uncertainty of propositions.