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In this paper, a new representation is presented for the Maximum Quartet Consistency (MQC) problem, where solving the MQC problem becomes searching for an ultrametric matrix that satisfies a maximum number of given quartet topologies. A number of structural properties of the MQC problem in this new representation are characterized through formulating into answer set programming, a recent powerful logic programming tool for modeling and solving search problems. Using these properties, a number of optimization techniques are proposed to speed up the search process. The experimental results on a number of simulated data sets suggest that the new representation, combined with answer set programming, presents a unique perspective to the MQC problem.