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

COMMUNITY is a formal approach to software architecture. It has a precise, yet intuitive mathematical semantics based on category theory. It supports, at the methodological level, a clear separation between computation, coordination, and distribution (including mobility). It provides a simple state-based language for describing component behaviour that is inspired by Unity and Interacting Processes. It also addresses composition as a first class concern and accounts for the emergence of global system properties from interconnections. This paper describes the approach and available tool support by modelling essential aspects of the GSM handover protocol. We also sketch a framework that we are implementing for the distributed execution of such specifications using Klava, a Java library for mobile agent systems based on tuple spaces.