# Modal Logics for Timed Control

Abstract : In this paper we use the timed modal logic $L_\nu$ to specify control objectives for timed plants. We show that the control problem for a large class of objectives can be reduced to a model-checking problem for an extension ($L^c$) of the logic Lnu with a new modality. More precisely we define a fragment of $L_\nu$, namely $L_\nu^d$, such that any control objective of $L_\nu^d$ can be translated into a $L^c$ formula that holds for the plant if and only if there is a controller that can enforce the control objective. We also show that the new modality of $L^c$ strictly increases the expressive power of $L_\nu$ while model-checking of Lc remains EXPTIME-complete.
Document type :
Conference papers

Cited literature [10 references]

https://hal.inria.fr/inria-00368581
Contributor : Franck Cassez <>
Submitted on : Tuesday, March 17, 2009 - 5:08:58 AM
Last modification on : Tuesday, March 30, 2021 - 12:12:08 PM
Long-term archiving on: : Tuesday, June 8, 2010 - 11:32:28 PM

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modal-control-concur05.pdf
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### Identifiers

• HAL Id : inria-00368581, version 1

### Citation

Patricia Bouyer, Franck Cassez, François Laroussinie. Modal Logics for Timed Control. 16th nt. onf. on oncurrency heory ('05), Aug 2005, San Francisco, United States. pp.81--94. ⟨inria-00368581⟩

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