Formalization, Mechanization and Automation of Gödel's Proof of God's Existence
This work provides a rigorous computational verification of a philosophical argument, which is incremental in applying existing theorem-proving techniques to a new domain.
The authors formalized, mechanized, and automated Gödel's ontological proof of God's existence using higher-order theorem provers, achieving automatic verification of consistency and demonstration of theorems with tools like Nitpick, LEO-II, Satallax, Coq, and Isabelle.
Gödel'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.