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An object-logic explanation for the inconsistency in Gödel’s ontological theory. (English) Zbl 1370.68258
Friedrich, Gerhard (ed.) et al., KI 2016: advances in artificial intelligence. 39th annual German conference on AI, Klagenfurt, Austria, September 26–30, 2016. Proceedings. Cham: Springer (ISBN 978-3-319-46072-7/pbk; 978-3-319-46073-4/ebook). Lecture Notes in Computer Science 9904. Lecture Notes in Artificial Intelligence, 244-250 (2016).
Summary: This paper discusses the inconsistency in Gödel’s ontological argument. Despite the popularity of Gödel’s argument, this inconsistency remained unnoticed until 2013, when it was detected automatically by the higher-order theorem prover Leo-II. Complementing the meta-logic explanation for the inconsistency available in our paper [“The inconsistency in Gödel’s ontological argument: a success story for AI in metaphysics”, in: Proceedings of the 25th international joint conference on artificial intelligence, IJCAI 2016, New York, NY, USA, July 09–15, 2016. Menlo Park, CA: AAAI Press. 936–942 (2016)], we present here a new purely object-logic explanation that does not rely on semantic argumentation.
For the entire collection see [Zbl 1347.68008].

MSC:
68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)
03A05 Philosophical and critical aspects of logic and foundations
Software:
LEO-II; PVS
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