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Reflection in Membership Equational Logic, Many-Sorted Equational Logic, Horn Logic with Equality, and Rewriting Logic

Authors
Journal
Electronic Notes in Theoretical Computer Science
1571-0661
Publisher
Elsevier
Publication Date
Volume
71
Identifiers
DOI: 10.1016/s1571-0661(05)82531-9
Keywords
  • Reflection
  • Reflective Logics
  • Universal Theory
  • Reflective Rewriting Logic
  • Reflective Membership Equational Logic
  • Reflective Horn Logic With Equality

Abstract

Abstract We show that the generalized variant of rewriting logic 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, and in particular for the Maude language itself.

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