In this paper we study several properties of the Exogenous Probabilistic Propositional Logic (EPPL), a logic for reasoning about probabilities, with the purpose of introducing a temporal version Exogenous Probabilistic Linear Temporal Logic (EPLTL). In detail, we give a small model theorem for EPPL and introduce a satisfaction and a model checking algorithm for both EPPL and EPLTL. We are also ...

Recently many process modelling approaches have been developed. However, in most of these approaches, it is often assumed that the processes in an organisation are clearly deened, and therefore the emphasis of process modelling is often put on the nal representation of the organisational process. However, in reality, processes are often not clearly deened. It is important to provide mechanisms ...

Quasi-star-free languages were first introduced and studied by Barrington, Compton, Straubing and Thérien within the context of circuit complexity in 1992, and their connections with propositional linear temporal logic were established by Ésik and Ito recently. While these results are all for finite words, in this paper we consider the languages on infinite words.

We outline a methodology for the modular speciication of telephone services within rst-order linear-time temporal logic. Typically, the services ooered by a telephone system consist of a basic service and several optional additional services, such as automatic callback, redirection, etc. We argue informally that temporal logic provides a exible formalism for the speciication of individual servi...

To counter a general belief that all the paradoxes stem from a kind of circularity (or involve some self–reference, or use a diagonal argument) Stephen Yablo designed a paradox in 1993 that seemingly avoided self–reference. We turn Yablo’s paradox, the most challenging paradox in the recent years, into a genuine mathematical theorem in Linear Temporal Logic (LTL). Indeed, Yablo’s paradox comes ...

Our objective is to extend the standard results of preservation and reflection of properties by bisimulations to the coalgebraic setting, as well as to study under what conditions these results hold for simulations. The notion of bisimulation is the classical one, while for simulations we use that proposed by Hughes and Jacobs. As for properties, we start by using a generalization of linear tem...

We use Tarski’s relational calculus to construct a model of linear temporal logic. Both discrete and dense time are covered and we obtain denotational domains for a large variety of reactive systems.

from [TW96]) We reveal an intimate connection between semidirect products of nite semigroups and substitution of formulas in linear temporal logic. We use this connection to obtain an algebraic characterization of the `until' hierarchy of linear temporal logic; the k-th level of that hierarchy is comprised of all temporal properties that are expressible by a formula of nesting depth k in the `u...

We present specification languages that naturally capture exactly the regular and ω-regular properties that are stutter invariant. Our specification languages are variants of the classical regular expressions and of the core of PSL, a temporal logic, which is widely used in industry and which extends the classical linear-time temporal logic LTL by semi-extended regular expressions.