On the expressiveness and monitoring of metric temporal logic

HO, H.M., OUAKNINE, J and WORRELL, J (2019). On the expressiveness and monitoring of metric temporal logic. Logical Methods in Computer Science, 15 (2), 13:1-13:52.

Preview

PDF 1803.02653.pdf - Published Version Creative Commons Attribution. Download (950kB) | Preview

Abstract

It is known that Metric Temporal Logic (MTL) is strictly less expressive than the Monadic First-Order Logic of Order and Metric (FO[<, +1]) when interpreted over timed words; this remains true even when the time domain is bounded a priori. In this work, we present an extension of MTL with the same expressive power as FO[<, +1] over bounded timed words (and also, trivially, over time-bounded signals). We then show that expressive completeness also holds in the general (time-unbounded) case if we allow the use of rational constants q ∈ Q in formulas. This extended version of MTL therefore yields a definitive real-time analogue of Kamp’s theorem. As an application, we propose a trace-length independent monitoring procedure for our extension of MTL, the first such procedure in a dense real-time setting.

Item Type:	Article
Uncontrolled Keywords:	0101 Pure Mathematics; 0803 Computer Software; 0802 Computation Theory and Mathematics
Identification Number:	https://doi.org/10.23638/LMCS-15(2:13)2019
Page Range:	13:1-13:52
SWORD Depositor:	Symplectic Elements
Depositing User:	Symplectic Elements
Date Deposited:	09 Oct 2019 16:32
Last Modified:	18 Mar 2021 03:26
URI:	https://shura.shu.ac.uk/id/eprint/25236

Actions (login required)

View Item

Downloads

Publication Metrics