In principle, bounded model checking (BMC) leads to semidecision procedures that can be used to verify liveness properties and to falsify safety properties. If the procedures fail, there is usually no information about the validity of the considered specification. In this paper, we present a new approach to BMC based on three-valued logic that allows us in many cases to falsify liveness properties and to verify safety properties. Moreover, we employ both global and local model checking to take advantage of the different types of specifications that can be handled by these techniques.