Proving the Absence Property Pattern Using the B Method

Dynamic properties are very useful in the specification of Information Systems (IS) and security policies. They allow the user to express properties that involve several states of a system. Indeed, invariance properties do not permit to cover such kind of properties. In this paper, we suggest a formal approach, based on the use of the B method, to verifying absence properties of the form Abs(P₂, From P₁ Until P₃) that express that some states, represented by predicate P₂, should not be reached starting from a state that satisfies P₁ until a state satisfies P₃ is reached. Our proposal consists in defining two proof obligations based on weakest preconditions that are sufficient and necessary to prove that a system verifies such a property.