A Normal Form for First-Order Temporal Formulae

In this paper a normal form for formulae of a first-order temporal logic is described. This normal form, called First-Order Separated Normal Form (SNFf), forms the basis of both a temporal resolution method [5] and a family of executable temporal logics [2]. A first-order temporal logic, based on a linear discrete model structure, is introduced and the procedure for transforming an arbitrary formula of this logic to SNFf is described. The transformation process not only preserves satisfiability but also ensures that any model of the transformed formula is a model of the original one. These properties ensure that the transformation into SNFf has applications in both theorem proving and execution.