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...

It is shown that a stutter-invariant property is expressible in Temporal Logic of Actions if and only if it is expressible in Second-order Temporal Logic. In particular, validity questions can be translated from one logic to the other. The proof is based on equivalence transformations between the formulas of Temporal Logic of Actions and Second-order Temporal Logic. The translation from Second-...

We develop a multi-modal/temporal logic for the analysis of a general class of continuous dynamical systems over arbitrary time-lines. Our frames consist of a topological space together with a flow (or group action), which is a function from the product of space and time into space that satisfies the two flow laws; we further require this function to be continuous. Over Euclidean space and real...

Kamp showed that linear temporal logic is expressively complete for first order logic over words. We give a Gabbay style proof to show that linear temporal logic extended with modulo counting and group quantifiers (introduced by Baziramwabo,McKenzie,Thérien) is expressively complete for first order logic with modulo counting (introduced by Straubing, Thérien, Thomas) and group quantifiers (intr...