On Explicit Reflection in Theorem Proving and Formal Verification

  • Sergei N. Artemov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1632)


We show that the stability requirement for a verication system yields the necessity of some sort of a reflection mechanism. However, the traditional reflection rule based on the Göodel implicit provability predicate leads to a “reflection tower” of theories which cannot be formally veried. We found natural lower and upper bounds on a metatheory capable of establishing stability of a given verication system. The paper also introduces an explicit reflection mechanism which can be veri ed internally. This circumvents the reflection tower and provides a theoretical justication for the verication process. On the practical side, the paper gives specic recommendations concerning verication of inference rules and building a veriable reflection mechanism for a theorem proving system.


Modal Logic Theorem Prove System Versus Computable Function High Order Logic 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Sergei N. Artemov
    • 1
  1. 1.Department of Computer ScienceCornell University IthacaUSA

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