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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)

Abstract

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.

Keywords

Modal Logic Theorem Prove System Versus Computable Function High Order 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.

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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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