In computer science jargon, a foundation ontology or upper ontology is a hierarchy of entities and associated rules that attempts to describe those general entities that do not belong to a specific problem domain. See ontology (computer science) for a more detailed description and examples.
In philosophy of mathematics, a foundation ontology is an ontology in the formal philosophical sense that is deemed to play a role in the foundations of mathematics. Most notably, the role played by Plato's ontology in some theories of realism in mathematics. Hilary Putnam made the distinction in 1975, arguing that one could believe in a realist philosophy of mathematical foundations without also accepting Plato's ontology or his sacred geometry, thus the labels "Platonist" and "realist" were not to be held equivalent.
This is discussed further in the article on foundations of mathematics.