From model checking to a temporal proof for partial models

Three-valued model checking has been proposed to support verification when some portions of the model are unspecified. Given a formal property, the model checker returns true if the property is satisfied, false and a violating behavior if it is not, maybe and a possibly violating behavior if it is possibly satisfied, i.e., its satisfaction may depend on how the unspecified parts are refined. Model checking, however, does not explain the reasons why a property holds, or possibly holds. Theorem proving can instead do it by providing a formal proof that explains why a property holds, or possibly holds in a system. Integration of theorem proving with model checking has only been studied for classical two-valued logic – hence, for fully specified models. This paper proposes a unified approach that enriches three-valued model checking with theorem proving to generate proofs which explain why true and maybe results are returned.