Abstract
The relationship between two well established formalisms for temporal reasoning is first investigated, namely between Allen’s interval algebra (or Allen’s temporal logic, abbreviated ATL) and linear temporal logic (LTL). A discrete variant of ATL is defined, called Allen linear temporal logic (ALTL), whose models are ω-sequences of timepoints. It is shown that any ALTL formula can be linearly translated into an equivalent LTL formula, thus enabling the use of LTL techniques on ALTL requirements. This translation also implies the NP-completeness of ATL satisfiability. Then the problem of monitoring ALTL requirements is investigated, showing that it reduces to checking satisfiability; the similar problem for unrestricted LTL is known to require exponential space. An effective monitoring algorithm for ALTL is given, which has been implemented and experimented with in the context of planning applications.
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References
Allen, J.: Towards a general theory of actions and time. Artificial Intelligence 23(2), 123–154 (1984)
Calvanese, D., De Giacomo, G., Vardi, M.Y.: Reasoning about actions and planning in LTL action theories. In: KR, pp. 593–602 (2002)
D’Amorim, M., Roşu, G.: Efficient monitoring of omega-languages. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 364–378. Springer, Heidelberg (2005)
Ghallab, M., Alaoui, A.M.: Managing efficiently temporal relations through indexed spanning trees. In: IJCAI, pp. 1297–1303 (1989)
Krokhin, A.A., Jeavons, P., Jonsson, P.: Reasoning about temporal relations: The tractable subalgebras of Allen’s interval algebra. J. ACM 50(5), 591–640 (2003)
Lacroix, S., Mallet, A., Bonnafous, D., Bauzil, G., Fleury, S., Herrb, M., Chatila, R.: Autonomous rover navigation on unknown terrains, functions and integration. International Journal of Robotics Research (2003)
Moskewicz, M., Madigan, C., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an Efficient SAT Solver. In: Design Automation Conference (DAC 2001) (June 2001)
Pnueli, A.: The temporal logic of programs. In: Proceedings of the 18th Annual Symposium on Foundations of Computer Science, New York. IEEE, Los Alamitos (1977)
Roşu, G., Bensalem, S.: Allen linear (interval) temporal logic – translation to LTL and monitor synthesis. Technical Report UIUCDCS-R-2006-2681, University of Illinois at Urbana-Champaign (January 2006)
Roşu, G., Havelund, K.: Rewriting-based techniques for runtime verification. J. of Automated Software Engineering 12(2), 151–197 (2005)
Sistla, A.P., Clarke, E.M.: The complexity of propositional linear temporal logics. J. ACM 32(3), 733–749 (1985)
Vilain, M., Kautz, H., van Beek, P.: Constraint propagation algorithms for temporal reasoning: a revised report. In: Readings in Qualitative Reasoning about Phyisical Systems. Morgan Kaufmann, Los Altos (1989)
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Roşu, G., Bensalem, S. (2006). Allen Linear (Interval) Temporal Logic – Translation to LTL and Monitor Synthesis. In: Ball, T., Jones, R.B. (eds) Computer Aided Verification. CAV 2006. Lecture Notes in Computer Science, vol 4144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11817963_25
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DOI: https://doi.org/10.1007/11817963_25
Publisher Name: Springer, Berlin, Heidelberg
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