Specifying Cyber Physical System Safety Properties with Metric Temporal Spatial Logic

Abstract

The safety properties of Cyber-Physical Systems have characteristics of both time and spatial attributes. Although various hybrid logic languages have been proposed to represent and reason properties with both time and spatial attributes, most of them are not concerned on the quantitative problem which is important for mission-critical CPSs to specify and verify safety properties. In this paper, we propose a language named metric temporal-spatial logic (MTSL) to solve the problem. MTSL is the combination result of the metric temporal logic (MTL) and the spatial logic S4u. It can represent and reason CPS safety properties with both temporal and spatial attributes in a time quantitative manner. Based on different expressivity requirements, we define two kinds of MTSL languages named MTSLtP C and MTSLtOC . Their computational complexity of satisfiability problem are analysed. Moreover, in order to construct a decidable metric temporal-spatial logic which can be used to define safety properties, we also point out that one may use safety metric temporal logic (SMTL) as the temporal language. The application of MTSLs are illustrated by case studies coming from transportation domain.

A spatio-temporal specification language and its completeness & decidability

“…Signals with E = B = {0, 1} are called Boolean signals, while these with E = R + are called real-valued or quantitative signals. A Boolean signal, transformed from real-valued one through a set of predicates, can be represented by MITL [31].…”

“…In order to express spatial changes in dense time, MTSL [31] is proposed to specify spatio-temporal properties of cyber-physical systems by integrating MTL with S4 u . They follow the traditional S4 u with truth value to specify spatial changes and extend the domain of time to realvalued interval within bounded time in the principle of PC and OC.…”

A Sound and Complete Axiomatisation for Spatio-Temporal Specification Language

“…Signals with E = B = {0, 1} are called Boolean signals, while those where E = R + are called realvalued or quantitative signals. A Boolean signal, transformed from real-valued one, can be represented by Metric Temporal Logic [8], [9]. The comparison of some temporal logics is listed in Table I.…”