Translating SUMO-K to Higher-Order Set Theory

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.

Converting the Suggested Upper Merged Ontology to Typed First-order Form

We describe the translation of the Suggested Upper Merged Ontology (SUMO) to Typed First-order Form (TFF) with level 0 polymorphism. Building on our prior work to create a TPTP FOF translation of SUMO for use in the E and Vampire theorem provers, we detail the transformations required to handle an explicitly typed logic, and express SUMO's type hierarchy for numbers in a manner consistent with its intended semantics and the three numerical classes allowed in TFF. We provide description of the open source code and an example proof in Vampire on the resulting theory.