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In air traffic control, two or more aircraft approaching each other within a close distance will create a conflict alert situation. To reduce the risk of mid-air collisions, a warning and resolution system is needed to issue alerts and provide maneuver resolutions. The current traffic-alert and collision avoidance system (TCAS) resolves potential conflicts by issuing directives for vertical maneuvers. A lot of research has been done to investigate the possibility of increasing airspace capacity by incorporating horizontal maneuvering of aircraft. This paper discusses a new approach to computing the horizontal maneuver resolutions. More specifically, symbolic reasoning about dynamic systems in conflict alert situations is used to derive resolution advisories.