A Normal Form for Temporal Logics and its Applications in Theorem-Proving and Execution

In this paper a normal form, called Separated Normal Form (SNF), for temporal logic formulae is described. A simple propositional temporal logic, based on a discrete linear model structure, is introduced and a procedure for transforming an arbitrary formula of this logic into SNF is described. It is shown that the transformation process preserves satisfiability and ensures that any model of the transformed formula is a model of the original one. This normal form not only provides a simple and concise representation for temporal formulae, but is also used as the basis for both a resolution proof method and an execution mechanism for this type of temporal logic. In addition to outlining these applications, we show how the normal form can be extended to deal with first-order temporal logic.