On the partial respects in which a real valued arithmetic system can verify its tableaux consistency

Authors:
Dan E. Willard
Affiliations:
State University of New York at Albany
Venue:
TABLEAUX'05 Proceedings of the 14th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
Year:
2005

Citing 4
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Abstract

Gödel’s Second Incompleteness Theorem states axiom systems of sufficient strength are unable to verify their own consistency. We will show this theorem does not preclude axiomizations for a computer’s floating point arithmetic from recognizing their own consistency, in certain well defined partial respects.