Skip to main content
SpringerLink
Log in

Refinement in hybridised institutions

  • Original Article
  • Published:
Formal Aspects of Computing

Abstract

Hybrid logics, which add to the modal description of transition structures the ability to refer to specific states, offer a generic framework to approach the specification and design of reconfigurable systems, i.e., systems with reconfiguration mechanisms governing the dynamic evolution of their execution configurations in response to both external stimuli or internal performance measures. A formal representation of such systems is through transition structures whose states correspond to the different configurations they may adopt. Therefore, each node is endowed with, for example, an algebra, or a first-order structure, to precisely characterise the semantics of the services provided in the corresponding configuration. This paper characterises equivalence and refinement for these sorts of models in a way which is independent of (or parametric on) whatever logic (propositional, equational, fuzzy, etc) is found appropriate to describe the local configurations. A Hennessy–Milner like theorem is proved for hybridised logics.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Agusti-Cullell J, Esteva F, Garcia P, Godo L (1990) Formalizing multiple-valued logics as institutions. In: Bouchon-Meunier B, Yager RR, Zadeh LA (eds) 3rd International conference on information processing and management of uncertainty in knowledge-based systems (IPMU 90, Paris, France, July 2–6, 1990). Lecture notes in computer science, vol 521. Springer, pp 269–278

  2. Areces C, ten Cate B (2006) Hybrid logics. In: Blackburn P, Wolter F, van Benthem J (eds) Handbook of modal logics. Elsevier, Amsterdam, pp 821–868

  3. Burstall R, Diaconescu R (1994) Hiding and behaviour: an institutional approach. In: Roscoe W (ed) A classical mind: essays in honour of C.A.R. Hoare. Prentice-Hall, Hertfordshire, pp 75–92

  4. Blackburn P, de Rijke M, Venema Y (2001) Modal logic. Number 53 in Cambridge Tracts in Theoretical Computer Science, Cambridge University Press, Cambridge

  5. Bidoit M, Hennicker R (2006) Constructor-based observational logic. J Logic Algebr Progr 67(1–2): 3–51

    Article  MATH  MathSciNet  Google Scholar 

  6. Beierle C, Kern-Isberner G (2005) Looking at probabilistic conditionals from an institutional point of view. In: Kern-Isberner G, Rödder W, Kulmann F (eds) Conditionals, information, and inference (revised selected papers of WCII 2002, Hagen, Germany, May 13–15, 2002). Lecture notes in computer science, vol 3301. Springer, pp 162–179

  7. Brauner T (2010) Hybrid logic and its proof-theory. Applied logic series, Springer, Netherlands

  8. Börger E, Stärk R (2003) Abstract state machines: a method for high-level system design and analysis. Springe, Berlin

    Book  Google Scholar 

  9. Blackburn P, Van Benthem J (2007) Modal logic: a semantic perspective. In: Blackburn P, Wolter F, van Benthem J (eds) Handbook of modal logic, studies in logic and practical reasoning, vol 3. Elsevier, Amsterdam, pp 1–82

  10. Cîrstea C (2006) An institution of modal logics for coalgebras. J Logic Algebr Progr 67(1–2):87–113

  11. Caleiro C, Mateus P, Sernadas A, Sernadas C (2006) Quantum institutions. In: Futatsugi K, Jouannaud J-P, Meseguer J (eds) Algebra, meaning, and computation, essays dedicated to Joseph A. Goguen on the occasion of his 65th birthday. Lecture notes in computer science, vol 4060. Springer, pp 50–64

  12. Diaconescu R (2008) Institution-independent model theory. studies in universal logic. Birkhäuser, Basel

    Google Scholar 

  13. Diaconescu R (2011) On quasi-varieties of multiple valued logic models. Math Log Q 57(2): 194–203

    Article  MATH  MathSciNet  Google Scholar 

  14. Diaconescu R, Madeira A (2014) Encoding hybridized institutions into first order logic. Math Struct Comput Sci. doi:10.1017/S0960129514000383

  15. Ehrig H, Mahr B (1985) Fundamentals of algebraic specification 1: equations and initial semantics. Monographs in theoretical computer science, an EATCS Series. Springer, Berlin

  16. Goguen JA, Burstall RM (1992) Institutions: abstract model theory for specification and programming. J ACM 39(1): 95–146

    Article  MATH  MathSciNet  Google Scholar 

  17. Gottwald S (2001) A treatise on many-valued logics. studies in logic and computation, vol 9. Research Studies Press, Baldock

  18. Grätzer G (1979) Universal algebra. Springer, New York

    MATH  Google Scholar 

  19. Hodges W (1997) A shorter model theory. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  20. Indrzejczak A (2007) Modal hybrid logic. Logic Log Philos 16: 147–257

    MATH  MathSciNet  Google Scholar 

  21. Madeira A (2013) Foundations and techniques for software reconfigurability. Ph.D. thesis, Universidades do Minho, Aveiro and Porto (Joint MAP-i Doctoral Programme)

  22. Madeira A, Faria JM, Martins MA, Barbosa LS (2011) Hybrid specification of reactive systems: an institutional approach. In: Barthe G, Pardo A, Schneider G (eds) Software engineering and formal methods (SEFM 2011, Montevideo, Uruguay, November 14–18, 2011). Lecture notes in computer science, vol 7041. Springer, pp 269–285

  23. Milner R (1989) Communication and concurrency. series in computer science. Prentice-Hall, Englewood Cliffs

  24. Madeira A, Martins MA, Barbosa LS (2013) Bisimilarity and refinement for hybrid(ised) logics. In: Derrick J, Boiten EA, Reeves S (eds) Refine-Proceedings 16th international refinement workshop. Electronic proceedings in theoretical computer science, vol 115, pp 84–98

  25. Martins MA, Madeira A, Diaconescu R, Barbosa LS (2011) Hybridization of institutions. In: Corradini A, KlIn B, Cîrstea C (eds) Algebra and coalgebra in computer science (CALCO 2011, Winchester, UK, August 30–September 2, 2011). Lecture notes in computer science, vol 6859. Springer, pp 283–297

  26. Mossakowski T, Maeder C, Lüttich K (2007) The heterogeneous tool set, Hets. In: Grumberg O, Huth M (eds) Tools and algorithms for the construction and analysis of systems (TACAS 2007-Braga, Portugal, March 24–April 1, 2007). Lecture notes in computer science, vol 4424. Springer, pp 519–522

  27. Madeira A, Neves R, Martins MA, Barbosa LS (2013) When even the interface evolves. In: Wang H, Banach R (eds) Proceedings of TASE (7th IEEE symposium on theoretical aspects of software engineering, Birmingham, July, 2013). IEEE Computer Society, pp 79–82

  28. Mossakowski T, Roggenbach M (2006) Structured CSP—a process algebra as an institution. In: Fiadeiro JL, Schobbens P-Y (eds) Recent trends in algebraic development techniques (revised selected papers of WADT 2006, La Roche en Ardenne, Belgium, June 1–3, 2006). Lecture notes in computer science, vol 4409. Springer, pp 92–110

  29. Neves R, Madeira A, Martins MA, Barbosa LS (2013) Hybridisation at work. In: Heckel R, Milius S (eds) Algebra and coalgebra in computer science—5th international conference, CALCO 2013, Warsaw, Poland, September 3–6, 2013. Proceedings, Lecture notes in computer science, vol 8089, Springer, pp 340–345

  30. Park D (1981) Concurrency and automata on infinite sequences. In: Deussen P (ed) Theoretical computer science (5th GI-conference, Karlsruhe, Germany, March 23–25, 1981). Lecture notes in computer science, vol 104. Springer, pp 167–183

  31. Sannella D (1999) Algebraic specification and program development by stepwise refinement. In: Bossi A (ed) Logic-based program synthesis and transformation. Lecture notes in computer science, vol 1817. Springer, Venezia, Italy, pp 1–9

  32. Sangiorgi D (2009) On the origins of bisimulation and coinduction. ACM Trans Progr Lang Syst 31(4):1–41. doi:10.1145/1516507.1516510

  33. Szepesia R, Ciocarlie H (2011) An overview on software reconfiguration. Theory Appl Math Comput Sci 1: 74–79

    Google Scholar 

  34. Schröder L, Mossakowski T (2009) HasCasl: integrated higher-order specification and program development. Theor Comput Sci 410(12–13): 1217–1260

    Article  MATH  Google Scholar 

  35. Sannella D, Tarlecki A (2012) Foundations of algebraic specification and formal software development. Monographs on theoretical computer science, an EATCS series. Springer

  36. Tarlecki A (2003) Abstract specification theory: an overview. In: Broy M, Pizka M (eds) Models, algebras, and logics of engineering software. NATO science series, computer and systems sciences, vol 191. IOS Press, pp 43–79

  37. ten Cate BD (2005) Model theory for extended modal languages. Ph.D. thesis, Institute for Logic, Language and Computation Universiteit van Amsterdam

Download references

Author information

Authors and Affiliations

  1. HASLab INESC TEC and Univ. Minho, Braga, Portugal

    Alexandre Madeira & Luís S. Barbosa

  2. CIDMA-Center for R&D in Mathematics and Applications, Department of Mathematics, Univ. Aveiro, Aveiro, Portugal

    Manuel A. Martins

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

    Rolf Hennicker

Authors
  1. Alexandre Madeira
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Manuel A. Martins
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Luís S. Barbosa
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Rolf Hennicker
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexandre Madeira.

Additional information

John Derrick, Steve Reeves, and Eerke Boiten

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Madeira, A., Martins, M.A., Barbosa, L.S. et al. Refinement in hybridised institutions. Form Asp Comp 27, 375–395 (2015). https://doi.org/10.1007/s00165-014-0327-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00165-014-0327-6

Keywords

Search

Navigation