In this paper, we introduce a real-time temporal knowledge logic, called RTKL, which is a combination of real-time temporal logic and knowledge logic. It is showed that temporal modalities such as “always in an interval”, “until in an interval”, and knowledge modalities such as “knowledge in an interval” and “common knowledge in an interval” can be expressed in such a logic. The model checking ...

This paper proposes an approach for mining multimodal temporal patterns from multiple synchronous signal sequences generated by different modalities. The instances of the temporal patterns suffer from noise and non-linear temporal warping. There are non-pattern signal segments separating the instances of the temporal patterns in the whole signal sequences. Hidden Markov models with thresholds o...

The common metric temporal logics for continuous time were shown to be insufficient, when it was proved in [7, 12] that they cannot express a modality suggested by Pnueli. Moreover no temporal logic with a finite set of modalities can express all the natural generalizations of this modality. The temporal logic with counting modalities (TLC ) is the extension of until-since temporal logic TL(U,S...

We add to the standard temporal logic with the modalities ”Until” and ”Since”, a sequence of “counting modalities”: For each n the modality Cn(X), which says that X will be true at least at n points in the next unit of time, and its past counterpart ←− C n, which says that X has happened at least n times in the last unit of time. We prove that this temporal logic is as expressive as can be hope...

Kamp’s theorem established the expressive equivalence of the temporal logic with Until and Since and the First-Order Monadic Logic of Order (FOMLO) over the Dedekind-complete time flows. However, this temporal logic is not expressively complete for FOMLO over the rationals. Stavi introduced two additional modalities and proved that the temporal logic with Until, Since and Stavi’s modalities is ...

We prove a conjecture by A. Pnueli and strengthen it showing a sequence of “counting modalities” none of which is expressible in the temporal logic generated by the previous modalities, over the real line, or over the positive reals. Moreover, there is no finite temporal logic that can express all of them over the real line, so that no finite metric temporal logic is expressively complete.