Model-Checking View-Based Partial Specifications

Michael Huth, Shekhar Pradhan

Abstract: We develop foundations for the view-based specification of software artifacts in first-order logic. Standard notions of models and semantics of first-order logic are generalized to partial models that do not have access to the entire global signature. At the model-theoretic level, this is achieved via the Smyth powerdomain over the semantic universe of elements. At the logical level, we accomplish this via the Smyth powerdomain over the standard two-valued booleans. A refinement notion is developed and its soundness is proved for a fixed set of semantic elements. Standard models and semantics of first-order logic are subsumed by our framework as models in which all signature information is present (“complete models”). We decompose our semantics into a consensus (the union of the Smyth powerdomain) of an optimistic and a pessimistic semantics. That way, we may compute this semantics as a standard model check in first-order logic over a model lifted by the Smyth powerdomain.