We add to the standard temporal logic TL(U,S) 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 dual ←− C n, which says that X has happened n times in the last unit of time. We show that this temporal logic is expressively complete for the metric predicate logic Q2MLO, which is expressive, de...

An intelligent agent, reasoning symbolically ill a continuous world, needs to infer properties of the behaviors of continuous systems. A qualitative simulator, such as QSI NI , con— structs a set. of possible behaviors corisis— tent with a qualitative differential equation (QDE) and initial state. This set of behaviors is expressed as a flinte tree of qualitative state descriptions. li-i the ca...

In the recent years, there have been a large amount of investigations on safety verification of uncertain continuous systems. In engineering and applied mathematics, this verification is called stochastic reachability analysis, while in computer science this is called probabilistic model checking (PMC). In the context of this work, we consider the two terms interchangeable. It is worthy to note...

Keywords: mathematical fuzzy logic, basic fuzzy logic, monoidal t-norm logic, hoop logic, non-commutative fuzzy logic. This paper is a companion to my [12]. The latter is a rather technical paper developing a generalized (mathematical) fuzzy logic. Main definitions and results of [12] are reproduced here without any proofs; but this is preceded by a survey on the basic proposi-tional fuzzy logi...

In this paper, we consider the robust interpretation of Metric Temporal Logic (MTL) formulas over signals that take values in metric spaces. For such signals, which are generated by systems whose states are equipped with non-trivial metrics, for example continuous or hybrid, robustness is not only natural, but also a critical measure of system performance. Thus, we propose multi-valued semantic...

This paper reviews two different uses of the continuous wavelet transform for modal identification purposes. The properties of the wavelet transform, mainly energetic, allow to emphasize or filter the main information within measured signals and thus facilitate the modal parameter identification especially when mechanical systems exhibit modal coupling and/or relatively strong damping.

This paper reviews two different uses of the continuous wavelet transform for modal identification purposes. The properties of the wavelet transform, mainly energetic, allow to emphasize or filter the main information within measured signals and thus facilitate the modal parameter identification especially when mechanical systems exhibit modal coupling and/or relatively strong damping.

The DIRECT algorithm is a deterministic sampling method for bound constrained Lipschitz continuous optimization. We prove a subsequential convergence result for the DIRECT algorithm that quantifies some of the convergence observations in the literature. Our results apply to several variations on the original method, including one that will handle general constraints. We use techniques from nons...

This paper reviews two different uses of the continuous wavelet transform for modal identification purposes. The properties of the wavelet transform, mainly energetic, allow to emphasize or filter the main information within measured signals and thus facilitate the modal parameter identification especially when mechanical systems exhibit modal coupling and/or relatively strong damping.