Towards a first-order modal formalisation of the unified foundational ontology

In this paper, we present a succinct formalisation of the main categories of the Unified Foundational Ontology (UFO) by summarising and simplifying a fragment of the version of [Gui05]. In this version, we show that the use first-order modal logic with no higher-order constructs suffices for many modelling tasks. We focus here on the case of universals.We slightly modify the original version of UFO by presenting new definitions of the intension and of the extension of universals and by approaching a taxonomy of universals.