Computable Kripke Models and Intermediate Logics

We introduce effectiveness considerations into model theory of intuitionistic logic. We investigate effectiveness of completeness (by Kripke) results for intermediate logics such as intuitionistic logic, classical logic, constant domain logic, directed frames logic, and Dummett's logic.     

Adaptive Verification using Forced Simulation

Simulation (a pre-order) over Kripke structures is a well known formal verification technique. Simulation guarantees that all behaviours of an abstracted structure (a property or function, F) are contained in a larger structure (a model M). A model, however, may not always simulate a property due to the presence of design errors. In this case, the model is debugged manually. In this paper, we propose a weaker simulation over structures called forced simulation for automated debugging. Forced simulation is applied when normal simulation fails. Forced simulation between a model (M) and a function (F) guarantees the existence of a modifier, D, to adapt M so that the composition of M and D is observationally equivalent to F. Observational equivalence over structures called weak bisimulation is developed in this paper. It is also established that when two structures are weakly bisimilar all CTL^* properties holding over one also holds over the other structure. Forced simulation based algorithm has been used to adapt many designs which had failed certain properties during conventional verification.