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Abstract: We show that the stability requirement for a verification system yields the necessity of some sort of a reection mechanism. However, the traditional reflection rule based on the Gödel implicit provability predicate leads to a "reflection tower" of theories which cannot be formally verified. We found natural lower and upper bounds on a metatheory capable of establishing stability of a given verification system. The paper introduces an explicit reflection mechanism which can be verified... (Update)
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BibTeX entry: (Update)
@inproceedings{ artemov99explicit,
author = "Sergei N. Artemov",
title = "On Explicit Reflection in Theorem Proving and Formal Verification",
booktitle = "Proceedings of the 16th International Conference on Automated Deduction ({CADE}-16)",
publisher = "Springer-Verlag LNAI 1632",
address = "Trento, Italy",
editor = "Harald Ganzinger",
pages = "267--281",
year = "1999",
url = "citeseer.ist.psu.edu/395139.html" }
Citations (may not include all citations):112 Constructivism in Mathematics (context) - Troelstra, van Dalen - 1988
42 Lecture Notes in Computer Science (context) - Pollack - 1995
31 Systems of Logics Based on Ordinals (context) - Turing - 1939
23 Self-Reference and Modal Logic (context) - Smorynski - 1985
22 The Incompleteness Theorems (context) - Smorynski - 1977
21 Formalized Metareasoning in Type Theory (context) - Knoblock, Constable - 1986
15 Metamathematical Extensibility for Theorem Veriers and Proof.. (context) - Davis, Schwartz - 1979
14 Operational Modal Logic - Artemov - 1995
13 The Unprovability of Consistency: An Essay in Modal Logic (context) - Boolos - 1979
9 Annals of Pure and Applied Logic (context) - Artemov - 1994
8 The Semantics of Re ected Proofs (context) - Allen, Constable et al. - 1990
6 Arithmetization of Metamathematics in a General Setting (context) - Feferman - 1960
5 Transnite Recursive Progressions of Axiomatic Theories (context) - Feferman - 1962
5 Metatheory and Re ection in Theorem Proving: A Survey and Cr.. (context) - Harrison - 1995
3 Explicit Provability: the Intended Semantics for Intuitionis.. - Artemov - 1998
3 The Basic Logic of Proofs - Artemov, Strassen - 1993
1 Re ection Principles and Their Use for Establishing the Comp.. (context) - Kreisel, Levy - 1968
1 Extensions of Theories by the Re ection Principles and the C.. (context) - Artemov - 1979
Documents on the same site (http://www.math.cornell.edu/~artemov/publ.html): More
Deep Isomorphism of Modal Derivations and λ-Terms - Artemov (1999) (Correct)
Logic of Proofs: a Unified Semantics for Modality and lambda-Terms - Artemov (1998) (Correct)
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