Translating SUMO-K to Higher-Order Set Theory

Chad Brown; Adam Pease; Josef Urban

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arXiv · 2305.07903

Translating SUMO-K to Higher-Order Set Theory

Chad Brown·Adam Pease·Josef Urban

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Abstract

We describe a translation from a fragment of SUMO (SUMO-K) into higher-order set theory. The translation provides a formal semantics for portions of SUMO which are beyond first-order and which have previously only had an informal interpretation. It also for the first time embeds a large common-sense ontology into a very secure interactive theorem proving system. We further extend our previous work in finding contradictions in SUMO from first order constructs to include a portion of SUMO's higher order constructs. Finally, using the translation, we can create problems that can be proven using higher-order interactive and automated theorem provers. This is tested in several systems and can be used to form a corpus of higher-order common-sense reasoning problems.

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Chad Brown, Adam Pease, Josef Urban. 2023-05-13. Translating SUMO-K to Higher-Order Set Theory. https://arxiv.org/abs/2305.07903

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