Abstract. This work exploits and extends the game-based framework of CTL model checking for counterexample and incremental abstraction-refinement. We define a game-based CTL model checking for abstract models over the 3-valued semantics, which can be used for verification as well as refutation. The model checking may end with an indefinite result, in which case we suggest a new notion of refinement, which eliminates indefinite results of the model checking. This provides an iterative abstraction-refinement framework. It is enhanced by an incremental algorithm, where refinement is applied only where indefinite results exist and definite results from prior iterations are used within the model checking algorithm. We also define the notion of annotated counterexamples, which are sufficient and minimal counterexamples for full CTL. We present an algorithm that uses the game board of the model checking game to derive an annotated counterexample in case the examined system model refutes the checked formula. 1

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models whose verification results transfer to the abstracted models for a logic with unrestricted use of negation and quantification. This framework is novel in that its models have quantitative or probabilistic observables and state transitions. Properties of a quantitative temporal logic have measurable denotations in these models. For probabilistic models such denotations approximate the probabilistic semantics of full LTL. We show how predicate-based abstractions specify abstract quantitative and probabilistic models with finite state space. 1