  We introduce a weight assignment logic for reasoning about quantitative
languages of infinite words. This logic is an extension of the classical MSO
logic and permits to describe quantitative properties of systems with multiple
weight parameters, e.g., the ratio between rewards and costs. We show that this
logic is expressively equivalent to unambiguous weighted B\"uchi automata. We
also consider an extension of weight assignment logic which is expressively
equivalent to nondeterministic weighted B\"uchi automata.
