Abstract. This paper explores reasoning about space and time, e.g., in metaphors of time as space; an important method is to find minimal assumptions needed to reach the same conclusions that humans reach. Some mathematical language, including the notion of triad, is introduced for this purpose, formalizing and generalizing the cognitive semantics approaches to conceptual spaces (in the senses of both Fauconnier & Turner and of Gärdenfors), blending, and metaphor; in particular, continuous mathematics is used to model space and time. A new explanation of emergent structure in blend spaces is also discussed, and proposed as a source of creativity. Four main examples illustrate the approach, and an appendix encapsulates the most difficult mathematics. 1

We propose a functional view of ontologies that emphasises their role in determining answers to queries, irrespective of the formalism in which they are written. A notion of framework is introduced that captures the situation of a global language into which both an ontology language and a query language can be translated, in an abstract way. We then generalise existing notions of robustness from the literature, and relate these to interpolation properties that support modularisation of ontologies.

Abstract. We propose a functional view of ontologies that emphasises their role in determining answers to queries, irrespective of the formalism in which they are written. A notion of framework is introduced that captures the situation of a global language into which both an ontology language and a query language can be translated, in an abstract way. We then generalise existing notions of robustness from the literature, and relate these to interpolation properties that support modularisation of ontologies.