Formal Aspects of Computing

, Volume 27, Issue 2, pp 375–395 | Cite as

Refinement in hybridised institutions

  • Alexandre MadeiraEmail author
  • Manuel A. Martins
  • Luís S. Barbosa
  • Rolf Hennicker
Original Article


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.


Hybridisation Bisimulation Refinement 


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  1. ACEGG90.
    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 269–278Google Scholar
  2. AtC06.
    Areces C, ten Cate B (2006) Hybrid logics. In: Blackburn P, Wolter F, van Benthem J (eds) Handbook of modal logics. Elsevier, Amsterdam, pp 821–868Google Scholar
  3. BD94.
    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 75–92Google Scholar
  4. BdRV01.
    Blackburn P, de Rijke M, Venema Y (2001) Modal logic. Number 53 in Cambridge Tracts in Theoretical Computer Science, Cambridge University Press, CambridgeGoogle Scholar
  5. BH06.
    Bidoit M, Hennicker R (2006) Constructor-based observational logic. J Logic Algebr Progr 67(1–2): 3–51CrossRefzbMATHMathSciNetGoogle Scholar
  6. BKI05.
    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 162–179Google Scholar
  7. Bra10.
    Brauner T (2010) Hybrid logic and its proof-theory. Applied logic series, Springer, NetherlandsGoogle Scholar
  8. BS03.
    Börger E, Stärk R (2003) Abstract state machines: a method for high-level system design and analysis. Springe, BerlinCrossRefGoogle Scholar
  9. BVB07.
    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 1–82Google Scholar
  10. C0̂6.
    Cîrstea C (2006) An institution of modal logics for coalgebras. J Logic Algebr Progr 67(1–2):87–113Google Scholar
  11. CMSS06.
    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 50–64Google Scholar
  12. Dia08.
    Diaconescu R (2008) Institution-independent model theory. studies in universal logic. Birkhäuser, BaselGoogle Scholar
  13. Dia11.
    Diaconescu R (2011) On quasi-varieties of multiple valued logic models. Math Log Q 57(2): 194–203CrossRefzbMATHMathSciNetGoogle Scholar
  14. DM14.
    Diaconescu R, Madeira A (2014) Encoding hybridized institutions into first order logic. Math Struct Comput Sci. doi: 10.1017/S0960129514000383
  15. EM85.
    Ehrig H, Mahr B (1985) Fundamentals of algebraic specification 1: equations and initial semantics. Monographs in theoretical computer science, an EATCS Series. Springer, BerlinGoogle Scholar
  16. GB92.
    Goguen JA, Burstall RM (1992) Institutions: abstract model theory for specification and programming. J ACM 39(1): 95–146CrossRefzbMATHMathSciNetGoogle Scholar
  17. Got01.
    Gottwald S (2001) A treatise on many-valued logics. studies in logic and computation, vol 9. Research Studies Press, BaldockGoogle Scholar
  18. Grä79.
    Grätzer G (1979) Universal algebra. Springer, New YorkzbMATHGoogle Scholar
  19. Hod97.
    Hodges W (1997) A shorter model theory. Cambridge University Press, CambridgezbMATHGoogle Scholar
  20. Ind07.
    Indrzejczak A (2007) Modal hybrid logic. Logic Log Philos 16: 147–257zbMATHMathSciNetGoogle Scholar
  21. Mad13.
    Madeira A (2013) Foundations and techniques for software reconfigurability. Ph.D. thesis, Universidades do Minho, Aveiro and Porto (Joint MAP-i Doctoral Programme)Google Scholar
  22. MFMB11.
    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 269–285Google Scholar
  23. Mil89.
    Milner R (1989) Communication and concurrency. series in computer science. Prentice-Hall, Englewood CliffsGoogle Scholar
  24. MMB13.
    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 84–98Google Scholar
  25. MMDB11.
    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 283–297Google Scholar
  26. MML07.
    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 519–522Google Scholar
  27. MNMB13.
    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 79–82Google Scholar
  28. MR06.
    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 92–110Google Scholar
  29. NMMB13.
    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 340–345Google Scholar
  30. Par81.
    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 167–183Google Scholar
  31. San99.
    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 1–9Google Scholar
  32. San09.
    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. SC11.
    Szepesia R, Ciocarlie H (2011) An overview on software reconfiguration. Theory Appl Math Comput Sci 1: 74–79Google Scholar
  34. SM09.
    Schröder L, Mossakowski T (2009) HasCasl: integrated higher-order specification and program development. Theor Comput Sci 410(12–13): 1217–1260CrossRefzbMATHGoogle Scholar
  35. ST12.
    Sannella D, Tarlecki A (2012) Foundations of algebraic specification and formal software development. Monographs on theoretical computer science, an EATCS series. SpringerGoogle Scholar
  36. Tar03.
    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 43–79Google Scholar
  37. tC05.
    ten Cate BD (2005) Model theory for extended modal languages. Ph.D. thesis, Institute for Logic, Language and Computation Universiteit van AmsterdamGoogle Scholar

Copyright information

© British Computer Society 2014

Authors and Affiliations

  • Alexandre Madeira
    • 1
    Email author
  • Manuel A. Martins
    • 2
  • Luís S. Barbosa
    • 1
  • Rolf Hennicker
    • 3
  1. 1.HASLab INESC TEC and Univ. MinhoBragaPortugal
  2. 2.CIDMA-Center for R&D in Mathematics and Applications, Department of MathematicsUniv. AveiroAveiroPortugal
  3. 3.Ludwig-Maximilians-Universität MünchenMunichGermany

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