Component breakdowns are a vital multi-purpose tool and hence ubiquitous across a range of disciplines. Information systems need to be capable of storing reasonably accurate representations of these breakdowns. Most current information systems have been designed around specific breakdowns, without considering their general underlying formal structure. This is understandable, given the focus on devising the breakdown and that there is not a readily available formal structure to build upon. We make a step towards providing this structure here.

At the core of the notion of a component breakdown is the component as an integral (dependent) part of the composite whole. This leads to a rich formal structure, one that requires careful consideration to capture well enough to support the range of specific breakdowns. If one is not sufficiently aware of this structure, it is difficult to determine what is required to produce a reasonably accurate representation – in particular, one that is sufficiently accurate to support interoperability.

In this report, enabled by the Construction Innovation Hub, we describe this rich formal structure and develop a framework for assessing how well a data model (or ontology) has captured the main elements of the structure. This will enable people to both assess existing models as well as design new models. As a separate exercise, as an illustration, we develop a data model that captures these elements.

Associated with the notion of component (as an integral, dependent part) is the notion of replaceable part (see Appendix A for more details). We do not characterise this here but will do so in a later report.

The purpose of this report is to give an understanding of the technicalities of the foundation and formalisation underpinning a foundational ontology.

This report is directed at a technical audience interested in understanding what the foundation of the foundational ontology is and how it is formalised. In particular, we expect the report to be of interest to logicians and formal ontologists.

This is part of a project to build a unified foundation, called the Core Constructional Ontology (CCO). This stage of the project has developed a transitional framework that establishes the feasibility of building the CCO. The framework is formalised by means of a theory we call the Core Constructional Theory (CCT). Here we describe the CCT and its associated CCO. Later stages of the project will further develop and enhance this framework. Appendix E.5 gives some indication of what these enhancements could be. This novel theory develops the idea that all the objects in the CCO emerge during construction. We start from an initial collection of objects—often called givens—and a small number of constructors, and the entire ontology unfolds from repeated constructions. So from the givens and constructors one knows, in principle, all the objects in the ontology. Using the technical resources of plural logic, the CCT formalises the arrangement of constructions in stages, where the intended ontology arises after exhausting all the stages. This report documents the CCT and provides a proof of its consistency.