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From Box Algebra to Interval Temporal Logic

Lookup NU author(s): Professor Maciej KoutnyORCiD, Dr Ben MoszkowskiORCiD



This is the authors' accepted manuscript of an article that has been published in its final definitive form by IOS Press, 2019.

For re-use rights please refer to the publisher's terms and conditions.


In this paper, we further develop a recently introduced semantic link between temporal logics and Petri nets. We focus on two specific formalisms, Interval Temporal Logic (ITL) and Box Algebra (BA), which are closely related by their compositional approach to constructing system descriptions. The overall goal of our investigation is to translate Petri nets into behaviourally equivalent logical formulas. As a result, the analysis of system properties can be carried out using either of the two formalisms, exploiting their respective strengths and powerful tool support.The contribution of this paper is twofold. First, we extend the existing translation from BA to ITL, by removing restrictions concerning the way control flow of concurrent system is modelled, and by allowing a fully generalsynchronisation operator. Second, we strengthen the notion of equivalence between a Petri net and the correspondinglogical formula by proving such an equivalence at the level of transition-based executions of Petri nets rather than just by looking at their labels. We also show that the complexity of the proposed translation compares favourably with the complexity of the translation from BA expressions to Petri nets.

Publication metadata

Author(s): Klaudel H, Koutny M, Duan Z, Moszkowski B

Publication type: Article

Publication status: Published

Journal: Fundamenta Informaticae

Year: 2019

Volume: 167

Issue: 4

Pages: 323-354

Online publication date: 05/07/2019

Acceptance date: 23/05/2019

Date deposited: 11/06/2019

ISSN (print): 1875-8681

ISSN (electronic): 0169-2968

Publisher: IOS Press


DOI: 10.3233/FI-2019-1820


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