In developing these techniques, temporal proof is often required, and we base our work on practical proof techniques for the clausal resolution method for propositional linear-time temporal logic PLTL. The method is based on an intuitive clausal form, called SNF, comprising three main clause types and a small number of resolution rules [11, 14]. While the approach has been shown to be competiti...

The modal μ-calculus is a very expressive temporal logic. In particular, logics such as LTL, CTL and CTL* can be translated into the modal μ-calculus, although existing translations of LTL and CTL* are at least exponential in size. We show that an existing simple first-order extension of the modal μ-calculus allows for a linear translation from LTL. Furthermore, we show that solving the transla...

We explore the concept of an agent-based Electronic Institution including a normative environment that supports electronic contract formation by providing a contextual normative background. We formalize the normative state using first-order logic and define institutional rules and norms operating on that state. A suitable semantics regarding the use of norms within a hierarchical context struct...

In this paper we consider branching time temporal logics of knowledge and belief. These logics involve the discrete time linear temporal logic operators “next” and “until” with the branching temporal logic operator “on all paths”. The latter operator is interpreted with respect to a version of the bundle semantics. In addition the temporal logic of knowledge (belief) contains an indexed set of ...

Monitoring temporal relationships among events in event streams has wide scale applicability in health information systems. From detecting violations of privacy policies in message sequences to diagnosing conditions in physiological data streams real-time event monitoring of temporal invariants is becoming an important tool for system design. We developed an Active Real-Time Event Monitoring an...

This paper investigates the applications of Labelled Deductive Systems (LDS) as a framework for the development of a computational formalism for the description of active historical databases. This formalism is then applied to the study of retroactive updates. The propositional temporal logic USV/Z for temporal validity is presented and we prove its soundness and completeness. The historical da...

Algebraization of computational logics in the theory of fork algebras has been a research topic for a while. This research allowed us to interpret classical first-order logic, several propositional monomodal logics, propositional and first-order dynamic logic, and propositional and first-order linear temporal logic in the theory of fork algebras. In this paper we formalize these interpretabilit...

In this paper we present a tableau calculus for a temporal extension of the description logic ALC, called T L ALC. This logic is based on the temporal language with`Until' interpreted over the natural numbers with expanding ALC-domains. The tableau calculus forms an elaborated combination of Wolper's tableau calculus for propositional linear temporal logic, the standard tableau-algorithm for AL...

We present a new proof of axiomatic completeness for Proposition Temporal Logic (PTL) for discrete, linear time for both finite and infinite time (without past-time). This makes use of a natural hierarchy of logics and notions and is an interesting alternative to the proofs in the literature based on tableaux, filtration, game theory and other methods. In particular we exploit the deductive com...

The paper presents an axiomatic system for quan-tiied propositional temporal logic (qptl), which is propositional temporal logic equipped with quantii-cation over propositions (boolean variables). The advantages of this extended temporal logic is that its expressive power is strictly higher than that of the un-quantiied version (ptl) and is equal to that of S1S, as well as that of !-automata. A...