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...

We present a formal framework based on metric temporal logic (MTL) for specifying and verifying real-time systems with a continuous environment. Metric temporal logic is extended to allow speciication of properties about duration of system's states. We prove that every formula of the duration calculus (DC) can be translated into an equivalent MTL-R formula. Expressiveness of DC and MTL-R are co...

In this paper, we present two Pythagorean fuzzy averaging aggregation operators such as, Pythagorean fuzzy weighted averaging (PFWA) operator, Pythagorean fuzzy ordered weighted averaging (PFOWA) operator and also introduce some of their basic properties.

Metric interval temporal logic (MITL) provides a tool to formulate high level tasks in an easy way. This allows to specify behaviour of a dynamical system in a given environment which lies beyond the scope of simple stabilization. Finding an input of the system which satisfies the MITL formula, demands new techniques and algorithms. In this thesis, a novel approach is presented which abstracts ...

In [14], we studied the computational behaviour of various first-order and modal languages interpreted in metric or weaker distance spaces. [13] gave an axiomatisation of an expressive and decidable metric logic. The main result of this paper is in showing that the technique of representing metric spaces by means of Kripke frames can be extended to cover the modal (hybrid) language that is expr...

We present a new translation of Metric Temporal Logic to the Linear Temporal Logic with a new set of the atomic propositions. We investigate a SAT-based bounded model checking method for Metric Temporal Logic that is interpreted over linear discrete infinite time models generated by discrete timed automata. We show how to implement the bounded model checking technique for Linear Temporal Logic ...

Positively weighted graphs have a natural intrinsic metric. We consider finite, positively weighted graphs with a positive lower bound for their minimal weights and show that any two such graphs, which are close enough with respect to the Gromov-Hausdorff metric, are equivalent as graphs.