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A framework for defining logics
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Introduction to HOL: a theorem proving environment for higher order logic
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Experience with FS100 as a framework theory
Papers presented at the second annual Workshop on Logical environments
General logics and logical frameworks
What is a logical system?
The Semantics of Predicate Logic as a Programming Language
Journal of the ACM (JACM)
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Theoretical Computer Science - Trees in algebra and programming
Structuring metatheory on inductive definitions
Information and Computation
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TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
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WADT '97 Selected papers from the 12th International Workshop on Recent Trends in Algebraic Development Techniques
A Fixedpoint Approach to Implementing (Co)Inductive Definitions
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
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CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
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LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Semantic Models for Distributed Object Reflection
ECOOP '02 Proceedings of the 16th European Conference on Object-Oriented Programming
Automatic verification of a model checker by reflection
PADL'06 Proceedings of the 8th international conference on Practical Aspects of Declarative Languages
ICTAC'05 Proceedings of the Second international conference on Theoretical Aspects of Computing
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A metalogical framework is a logic with an associated methodology that is used to represent other logics and to reason about their metalogical properties. We propose that logical frameworks can be good metalogical frameworks when their logics support reflective reasoning and their theories always have initial models. We present a concrete realization of this idea in rewriting logic. Theories in rewriting logic always have initial models and this logic supports reflective reasoning. This implies that inductive reasoning is valid when proving properties about the initial models of theories in rewriting logic, and that we can use reflection to reason at the metalevel about these properties. In fact, we can uniformly reflect induction principles for proving metatheorems about rewriting logic theories and their parameterized extensions. We show that this reflective methodology provides an effective framework for different, non-trivial, kinds of formal metatheoretic reasoning; one can, for example, prove metatheorems that relate theories or establish properties of parameterized classes of theories. Finally, we report on the implementation of an inductive theorem prover in the Maude system, whose design is based on the results presented in this paper.