The semantic processing of continuous quantities for discrete terms in ontologies

We consider continuous quantities that are used to describe the physical world, such as colour, shape, sound, texture and spatial and temporal arrangements. Natural languages are not adept at describing these quantities, nor are they easily incorporated into ontologies in the form of discrete terms. In this article, we analyse the way that natural languages handle continuous quantities, propose a general semantics based on metric spaces, and describe how to treat semantic values computationally, so that we may automate the processing of texts which describe continuous quantities allowing, for example, query evaluation and the integration of multiple texts. This provides a basis for incorporating these quantities into ontologies and combining their semantics with automated reasoning tools. We run a series of experiments to evaluate the semantics, the general framework, and the computational system we have developed.