A hierarchy of partial order temporal properties

Marta Kwiatkowska; Doron Peled; Wojciech Penczek

doi:10.1007/bfb0014001

A hierarchy of partial order temporal properties

Marta Kwiatkowska, Doron Peled, Wojciech Penczek

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

We propose a classification of partial order temporal properties into a hierarchy, which is a generalization of the safety-progress hierarchy of Chang, Manna and Pnueli. The classes of the hierarchy are characterized through three views: language-theoretic, topological and temporal. Instead of the domain of strings, we take the domain of Mazurkiewicz traces as a basis for our considerations. For the language-theoretic view, we propose operations on trace languages which define the four main classes of properties: safety, guarantee, persistence and response. These four classes are shown to correspond precisely to the two lower levels of the Borel hierarchy of the Scott topology of the domain of traces relativized to the infinite traces. In addition, a syntactic characterization of the classes is provided in terms of a sublogic of the Generalized Interleaving Set Temporal Logic GISTL (an extension of ISTL).

Original language	English
Title of host publication	Temporal Logic - 1st International Conference, ICTL 1994, Proceedings
Editors	Dov M. Gabbay, Hans Jurgen Ohlbach
Publisher	Springer Verlag
Pages	398-414
Number of pages	17
ISBN (Print)	9783540582410
DOIs	https://doi.org/10.1007/bfb0014001
State	Published - 1994
Externally published	Yes
Event	1st International Conference on Temporal Logic, ICTL 1994 - Bonn, Germany Duration: 11 Jul 1994 → 14 Jul 1994

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	827 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	1st International Conference on Temporal Logic, ICTL 1994
Country/Territory	Germany
City	Bonn
Period	11/07/94 → 14/07/94

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1994.

Funding

Central to both approaches is the space Z ~ of infinite strings (words) over a given alphabet Z. Each infinite string (of states or events) models a possible * Supported in part by CEC grant CIPA3510PL927369. Visiting Academic at the Department of Computing, Imperial College, for the duration of the Nuffield Science Foundation Fellowship SCI/124/528/G. ** On leave from Institute of Computer Science, PAS, Warsaw, Poland. Supported in part by CEC grant CIPA3510PL927370 and by the Polish grant No. 2 2047 9203.

Funders	Funder number
Indian Institute of Science
FP7 Space	CIPA3510PL927369
Nuffield Foundation	SCI/124/528/, SCI/124/528/G.
Polska Akademia Nauk	2 2047 9203, 2047 9203
Birla Institute of Technology and Science, Pilani	CIPA3510PL927370

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10.1007/bfb0014001

Cite this

Kwiatkowska, M., Peled, D., & Penczek, W. (1994). A hierarchy of partial order temporal properties. In D. M. Gabbay, & H. J. Ohlbach (Eds.), Temporal Logic - 1st International Conference, ICTL 1994, Proceedings (pp. 398-414). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 827 LNAI). Springer Verlag. https://doi.org/10.1007/bfb0014001

Kwiatkowska, Marta ; Peled, Doron ; Penczek, Wojciech. / A hierarchy of partial order temporal properties. Temporal Logic - 1st International Conference, ICTL 1994, Proceedings. editor / Dov M. Gabbay ; Hans Jurgen Ohlbach. Springer Verlag, 1994. pp. 398-414 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Kwiatkowska, M, Peled, D & Penczek, W 1994, A hierarchy of partial order temporal properties. in DM Gabbay & HJ Ohlbach (eds), Temporal Logic - 1st International Conference, ICTL 1994, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 827 LNAI, Springer Verlag, pp. 398-414, 1st International Conference on Temporal Logic, ICTL 1994, Bonn, Germany, 11/07/94. https://doi.org/10.1007/bfb0014001

A hierarchy of partial order temporal properties. / Kwiatkowska, Marta; Peled, Doron; Penczek, Wojciech.
Temporal Logic - 1st International Conference, ICTL 1994, Proceedings. ed. / Dov M. Gabbay; Hans Jurgen Ohlbach. Springer Verlag, 1994. p. 398-414 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 827 LNAI).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - We propose a classification of partial order temporal properties into a hierarchy, which is a generalization of the safety-progress hierarchy of Chang, Manna and Pnueli. The classes of the hierarchy are characterized through three views: language-theoretic, topological and temporal. Instead of the domain of strings, we take the domain of Mazurkiewicz traces as a basis for our considerations. For the language-theoretic view, we propose operations on trace languages which define the four main classes of properties: safety, guarantee, persistence and response. These four classes are shown to correspond precisely to the two lower levels of the Borel hierarchy of the Scott topology of the domain of traces relativized to the infinite traces. In addition, a syntactic characterization of the classes is provided in terms of a sublogic of the Generalized Interleaving Set Temporal Logic GISTL (an extension of ISTL).

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Kwiatkowska M, Peled D, Penczek W. A hierarchy of partial order temporal properties. In Gabbay DM, Ohlbach HJ, editors, Temporal Logic - 1st International Conference, ICTL 1994, Proceedings. Springer Verlag. 1994. p. 398-414. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/bfb0014001

A hierarchy of partial order temporal properties

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