Reflection in membership equational logic, many-sorted equational logic, Horn logic with equality, and rewriting logic

  • Authors:
  • Manuel Clavel;José Meseguer;Miguel Palomino

  • Affiliations:
  • Departamento de Sistemas Informáticos y Computación, Universidad Complutense de Madrid, C/ Profesor García Santesmases, 28040, Madrid, Spain;Computer Science Department, University of Illinois at Urbana-Champaign, Thomas M. Siebel Center for Computer Science, 201 N. Goodwin, Urbana, IL 61801-2302, United States;Departamento de Sistemas Informáticos y Computación, Universidad Complutense de Madrid, C/ Profesor García Santesmases, 28040, Madrid, Spain

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2007

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Abstract

We show that the generalized variant of formal systems where the underlying equational specifications are membership equational theories, and where the rules are conditional and can have equations, memberships and rewrites in the conditions is reflective. We also show that membership equational logic, many-sorted equational logic, and Horn logic with equality are likewise reflective. These results provide logical foundations for reflective languages and tools based on these logics.