On Explicit Reflection in Theorem Proving and Formal Verification
نویسنده
چکیده
The basic properties of soundness, extensibility, and stability required from a verification system V taken in full yield the necessity of having a reflection rule in every such V. However, the reflection rule based on the Gödel provability predicate (implicit provability predicate) leads to a "reflection tower" of theories which cannot be formally verified. The paper introduces an explicit reflection mechanism which can be verified inside the system. This circumvents the reflection tower and provides a strict justification for the verification process. On the practical side, the paper gives specific recommendations concerning the verification of inference rules and building a verifiable reflection mechanism for a theorem proving system.
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