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This paper examines FLC, which is the modal 碌-calculus enriched with a sequential composition operator. Bisimulation invariance and the tree model property are proved. Its succinctness is compared to the modal 碌-calculus. The main focus lies on FLC's model checking problem over finite transition systems. It is proved to be PSPACE-hard. A tableau model checker is given and an upper EXPTIME bound is derived from it. For a fixed alternation depth FLC's model checking problem turns out to be PSPACE-complete.