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Dynamic Logic with Binders and Its Application to the Development of Reactive Systems

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Theoretical Aspects of Computing – ICTAC 2016 (ICTAC 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9965))

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Abstract

This paper introduces a logic to support the specification and development of reactive systems on various levels of abstraction, from property specifications, concerning e.g. safety and liveness requirements, to constructive specifications representing concrete processes. This is achieved by combining binders of hybrid logic with regular modalities of dynamic logics in the same formalism, which we call \(\mathcal {D}^{\downarrow }\)-logic. The semantics of our logic focuses on effective processes and is therefore given in terms of reachable transition systems with initial states. The second part of the paper resorts to this logic to frame stepwise development of reactive systems within the software development methodology proposed by Sannella and Tarlecki. In particular, we instantiate the generic concepts of constructor and abstractor implementations by using standard operators on reactive components, like relabelling and parallel composition, as constructors, and bisimulation for abstraction. We also study vertical composition of implementations which relies on the preservation of bisimularity by the constructions on labeleld transition systems.

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Notes

  1. 1.

    See translator.nrc.pt.

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Acknowledgments

This work is financed by the ERDF European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT - Fundação para a Ciência Tecnologia within project POCI-01-0145-FEDER-016692 and UID/MAT/04106/2013 at CIDMA. A. Madeira and L. S. Barbosa are further supported by FCT individual grants SFRH/BPD/103004/2014 and SFRH/BSAB/113890/2015, respectively.

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Authors and Affiliations

  1. HASLab INESC TEC, University of Minho, Braga, Portugal

    Alexandre Madeira & Luis S. Barbosa

  2. Ludwig-Maximilians-Universität München, Munich, Germany

    Rolf Hennicker

  3. CIDMA - Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Manuel A. Martins

Authors
  1. Alexandre Madeira
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  2. Luis S. Barbosa
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  3. Rolf Hennicker
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  4. Manuel A. Martins
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Correspondence to Alexandre Madeira .

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Editors and Affiliations

  1. Universidade Federal de Pernambuco Centro de Informática, Recife, Pernambuco, Brazil

    Augusto Sampaio

  2. Deptartment of Electrical Engineering BL, National Taiwan University, Taipei, Taiwan

    Farn Wang

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Madeira, A., Barbosa, L.S., Hennicker, R., Martins, M.A. (2016). Dynamic Logic with Binders and Its Application to the Development of Reactive Systems. In: Sampaio, A., Wang, F. (eds) Theoretical Aspects of Computing – ICTAC 2016. ICTAC 2016. Lecture Notes in Computer Science(), vol 9965. Springer, Cham. https://doi.org/10.1007/978-3-319-46750-4_24

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  • DOI: https://doi.org/10.1007/978-3-319-46750-4_24

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  • Print ISBN: 978-3-319-46749-8

  • Online ISBN: 978-3-319-46750-4

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