The FOUnt ontologies for quantities, units, and the physical world

Quantities and units of measure provide an important means by which intelligent agents interact with the physical world. Although multiple ontologies for quantities and units of measure have been proposed within the Applied Ontology com-munity, they often incorporate questionable ontological commitments. Quantities are combined using notions of dimensional analysis that often conflate the combination of units with algebraic operations on real numbers. In this paper, we present an alternative approach that shifts the focus to the connection between kinds of measurements associated with a unit and the phys-ical objects and processes that are being measured. One of the key features of this approach is that it makes minimal ontological commitments with respect to the TUpper upper ontology - the only new classes that are introduced are the classes for kinds of measures and associated units. We propose axiomatizations of the intended semantics for combining measurements, and the correct axiomatization of the relationship between the quantities and units of measure and the existing upper ontology.