Parameterized Metareasoning in Membership Equational Logic

  • Manuel Clavel
  • Narciso Martí-Oliet
  • Miguel Palomino
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7000)


Basin, Clavel, and Meseguer showed in [1] that membership equational logic is a good metalogical framework because of its initial models and support of reflective reasoning. A development and an application of those ideas was presented later in [4]. Here we further extend the metalogical reasoning principles proposed there to consider classes of parameterized theories and apply this reflective methodology to the proof of different parameterized versions of the deduction theorem for minimal logic of implication.


Parameterized Theory Atomic Formula Universal Theory Ground Term Minimal Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Basin, D., Clavel, M., Meseguer, J.: Reflective metalogical frameworks. ACM Transactions on Computational Logic 5(3), 528–576 (2004)Google Scholar
  2. 2.
    Basin, D., Matthews, S.: Structuring metatheory on inductive definitions. Information and Computation 162(1/2), 80–95 (2000)Google Scholar
  3. 3.
    Bouhoula, A., Jouannaud, J.-P., Meseguer, J.: Specification and proof in membership equational logic. Theoretical Computer Science 236, 35–132 (2000)Google Scholar
  4. 4.
    Clavel, M., Martí-Oliet, N., Palomino, M.: Formalizing and proving semantic relations between specifications by reflection. In: Rattray, C., Maharaj, S., Shankland, C. (eds.) AMAST 2004. LNCS, vol. 3116, pp. 72–86. Springer, Heidelberg (2004)Google Scholar
  5. 5.
    Clavel, M., Meseguer, J.: Axiomatizing reflective logics and languages. In: Kiczales, G. (ed.) Proceedings of Reflection 1996, San Francisco, California, pp. 263–288 (April 1996)Google Scholar
  6. 6.
    Clavel, M., Meseguer, J., Palomino, M.: Reflection in membership equational logic, many-sorted equational logic, Horn-logic with equality, and rewriting logic. Theoretical Computer Science 373(1-2), 70–91 (2007)Google Scholar
  7. 7.
    Clavel, M., Palomino, M., Riesco, A.: Introducing the ITP tool: A tutorial. Journal of Universal Computer Science 12(11), 1618–1650 (2006); Special issue with extended versions of selected papers from PROLE 2005: The Fifth Spanish Conference on Programming and LanguagesGoogle Scholar
  8. 8.
    Feferman, S.: Finitary inductively presented logics. In: Ferro, R., Bonotto, C., Valentini, S., Zanardo, A. (eds.) Logic Colloquium 1988, pp. 191–220. North-Holland (1989)Google Scholar
  9. 9.
    Goguen, J., Burstall, R.: Institutions: Abstract model theory for specification and programming. Journal of the Association for Computing Machinery 39(1), 95–146 (1992)Google Scholar
  10. 10.
    Meseguer, J.: Membership algebra as a logical framework for equational specification. In: Parisi-Presicce, F. (ed.) WADT 1997. LNCS, vol. 1376, pp. 18–61. Springer, Heidelberg (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Manuel Clavel
    • 1
  • Narciso Martí-Oliet
    • 1
  • Miguel Palomino
    • 1
  1. 1.Departamento de Sistemas Informáticos y ComputaciónUniversidad Complutense de MadridSpain

Personalised recommendations