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Formalization, Mechanization and Automation of Gödel's Proof of God's Existence

European Conference on Artificial Intelligence (ECAI), 2013
21 August 2013
Christoph Benzmüller
B. W. Paleo
ArXiv (abs)PDFHTML
Abstract

G\"odel's ontological proof has been analysed for the first-time with an unprecedent degree of detail and formality with the help of theorem provers. The following has been done (and in this order): A detailed natural deduction proof. A formalization of the axioms, definitions and theorems in the TPTP THF syntax. Automatic verification of the consistency of the axioms and definitions with Nitpick. Automatic demonstration of the theorems with the provers LEO-II and Satallax. A step-by-step formalization using the Coq proof assistant. A formalization using the Isabelle proof assistant, where the theorems (and some additional lemmata) have been automated with Sledgehammer and Metis.

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