The Fantastic Combinations and Permutations of Coordinate Systems' Characterising Options

The Game of Constructional Ontology

The multi-level modelling community’s raison d'être is its vision of the ubiquity and importance of multi-level-types: the ascending levelled hierarchy of types in conceptual models; starting with types of things, then types of these types, then types of these types of types, and so on. The community both promotes this vision and investigates this hierarchy, looking at how it can be accommodated into existing frameworks. In this paper, we consider a specific domain, coordinate systems’ characterising options. While we recognise that, unsurprisingly, this domain contains a ubiquity of multi-level-types, our interest is in investigating a new and different approach to understanding them. For this we needed to develop a new framework. We devise one focussing on this case, based upon scaling down to simple compositional algorithms (called constructors) to form a new, radically simpler foundation. From the simple operations of these constructors emerges the scaled up multi-level structures of the domain. We show how the simple operations of simple constructors give rise to compositional connections that shape – and so explain – different complex hierarchies and levels, including the familiar multi-level-types and relatively unknown multi-level-tuples. The framework crystallises these connections as metaphysical grounding relations. We look at how simple differences in the shape and operation of constructors give rise to different varieties of these hierarchies and levels – and the impact this has. We also look at how the constructional approach reveals the differences between foundational constructors and derived constructors built from the foundational constructors – and show that conceptual modeling’s generalisation relations are secondary and dependent upon the more foundational instantiation relations. Based upon this, we assemble a constructional foundational ontology using the BORO Foundational Ontology as our starting point. We then use this to reveal and explain the formal levels and hierarchies that underlie the options for characterising coordinate systems.