Continuous time temporal logic with counting

Continuous time temporal logic with counting

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...

Counting Models of Linear-Time Temporal Logic

We investigate the model counting problem for safety specifications expressed in linear-time temporal logic (LTL). Model counting has previously been studied for propositional logic; in planning, for example, propositional model counting is used to compute the plan’s robustness in an incomplete domain. Counting the models of an LTL formula opens up new applications in verification and synthesis...

Metric Temporal Logic with Counting

Ability to count number of occurrences of events within a specified time interval is very useful in specification of resource bounded real time computation. In this paper, we study an extension of Metric Temporal Logic (MTL) with two different counting modalities called C and UT (until with threshold), which enhance the expressive power of MTL in orthogonal fashion. We confine ourselves only to...

Monitoring Dense-Time, Continuous-Semantics, Metric Temporal Logic

Robustness of temporal logic specifications for continuous-time signals

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...