Automating Gödel's Ontological Proof of God's Existence with Higher-order Automated Theorem Provers

The Inconsistency in Gödel's Ontological Argument: A Success Story for AI in Metaphysics

This paper discusses the discovery of the inconsistency in Gödel’s ontological argument as a success story for artificial intelligence. Despite the popularity of the argument since the appearance of Gödel’s manuscript in the early 1970’s, the inconsistency of the axioms used in the argument remained unnoticed until 2013, when it was detected automatically by the higher-order theorem prover Leo-...

Proof Critics for IsaPlanner

The discovery of missing lemmas and case-splits are challenging problems for automated theorem proving. Most interactive provers rely on the user for guidance through these proof-steps. Proof-planning critics were introduced by Ireland as a way of automating this. Here, we present ongoing work developing critics for lemma speculation and caseanalysis in higher-order logic in the IsaPlanner system.

Overview on Leo-ii Leo-ii and Tptp

LEO-II is a standalone, resolution-based higher-order theorem prover that is designed for fruitful cooperation with specialist provers for first-order and propositional logic. The idea is to combine the strengths of the different systems. On the other hand, LEO-II itself, as an external reasoner, wants to support interactive proof assistants such as Isabelle/HOL, HOL, and OMEGA by efficiently a...

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

Computer-Assisted Analysis of the Anderson-Hájek Ontological Controversy

We present an exemplary study in Computational Metaphysics, which is an emerging, interdisciplinary field aiming at the rigorous formalisation and deep logical assessment of rational, philosophical arguments on the computer. The particular focus here is on the ontological argument for the existence of God. While related work [9, 7] has concentrated on Anselm’s simpler original version of the on...