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We present CLTLB(D), an extension of PLTLB (PLTL with both past and futureoperators) augmented with atomic formulae built over a constraint system D.Even for decidable constraint systems, satisfiability and Model Checkingproblem of such logic can be undecidable. We introduce suitable restrictionsand assumptions that are shown to make the satisfiability problem for theextended logic decidable. Moreover for a large class of constraint systems wepropose an encoding that realize an effective decision procedure for theBounded Reachability problem.

Bounded Reachability for Temporal Logic over Constraint Systems