Proof of the Existence of God, according Goedel Theorem

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

Christoph Benzmüller, Bruno Woltzenlogel Paleo

(Submitted on 21 Aug 2013 (v1), last revised 10 Sep 2013 (this version, v4))

Goedel's ontological proof has been analysed for the first-time with an unprecedent degree of detail and formality with the help of higher-order 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.

Comments:	2 pages
Subjects:	Logic in Computer Science (cs.LO); Artificial Intelligence (cs.AI); Logic (math.LO)
MSC classes:	03Axx, 68T27, 68T30, 68T15
ACM classes:	F.4.1; I.2.3; I.2.4
Cite as:	arXiv:1308.4526 [cs.LO]
	(or arXiv:1308.4526v4 [cs.LO] for this version) Download: PDF PostScript Other formats Source: Archiv