Fragment Of Metric Temporal Logic Research Articles

Runtime verification of autopilot systems using a fragment of MTL- $${\int }$$ ∫

Current real-time embedded systems development frameworks lack support for the verification of properties using explicit time where counting time (i.e., durations) may play an important role in the development process. Focusing on the real-time constraints inherent to these systems, we present a framework that addresses the specification of duration properties for runtime verification by employing a fragment of metric temporal logic with durations. We also provide an overview of the framework, the synthesis tools, and the library to support monitoring properties for real-time systems developed in C++11. The results obtained provide clear evidence of the feasibility and advantages of employing a duration-sensitive formalism to increase the dependability of avionic controller systems such as the PX4 and the Ardupilot flight stacks.

Ontology-Based Data Access with a Horn Fragment of Metric Temporal Logic

We advocate datalogMTL, a datalog extension of a Horn fragment of the metric temporal logic MTL, as a language for ontology-based access to temporal log data. We show that datalogMTL is EXPSPACE-complete even with punctual intervals, in which case MTL is known to be undecidable. Nonrecursive datalogMTL turns out to be PSPACE-complete for combined complexity and in AC0 for data complexity. We demonstrate by two real-world use cases that nonrecursive datalogMTL programs can express complex temporal concepts from typical user queries and thereby facilitate access to log data. Our experiments with Siemens turbine data and MesoWest weather data show that datalogMTL ontology-mediated queries are efficient and scale on large datasets of up to 11GB.

On termination and invariance for faulty channel machines

Abstract A channel machine consists of a finite controller together with several fifo channels; the controller can read messages from the head of a channel and write messages to the tail of a channel. In this paper we focus on channel machines with insertion errors , i.e., machines in whose channels messages can spontaneously appear. We consider the invariance problem: does a given insertion channel machine have an infinite computation all of whose configurations satisfy a given predicate? We show that this problem is primitive-recursive if the predicate is closed under message losses. We also give a non-elementary lower bound for the invariance problem under this restriction. Finally, using the previous result, we show that the satisfiability problem for the safety fragment of Metric Temporal Logic is non-elementary.

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 semantics for MTL formulas, which capture not only the usual Boolean satisfiability of the formula, but also topological information regarding the distance, ε , from unsatisfiability. We prove that any other signal that remains ε -close to the initial one also satisfies the same MTL specification under the usual Boolean semantics. Finally, our framework is applied to the problem of testing formulas of two fragments of MTL, namely Metric Interval Temporal Logic (MITL) and closed Metric Temporal Logic (clMTL), over continuous-time signals using only discrete-time analysis. The motivating idea behind our approach is that if the continuous-time signal fulfills certain conditions and the discrete-time signal robustly satisfies the temporal logic specification, then the corresponding continuous-time signal should also satisfy the same temporal logic specification.

An infinitary variant of Metric Temporal Logic over dense time domains

AbstractWe introduce a complete and cut‐free proof system for a sufficiently expressive fragment of Metric Temporal Logic over dense time domains in which a schema of induction is provable. So doing we extend results previously obtained by Montagna et al. to unbounded temporal operators. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)