Abstract
AbstractWe present an abstract development of Gödel’s incompleteness theorems, performed with the help of the Isabelle/HOL proof assistant. We analyze sufficient conditions for the applicability of our theorems to a partially specified logic. In addition to the usual benefits of generality, our abstract perspective enables a comparison between alternative approaches from the literature. These include Rosser’s variation of the first theorem, Jeroslow’s variation of the second theorem, and the Świerczkowski–Paulson semantics-based approach. As part of the validation of our framework, we upgrade Paulson’s Isabelle proof to produce a mechanization of the second theorem that does not assume soundness in the standard model, and in fact does not rely on any notion of model or semantic interpretation.
Publisher
Springer Science and Business Media LLC
Subject
Artificial Intelligence,Computational Theory and Mathematics,Software
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