Pattern:Mereology Pattern

Description

An English description of the definition (what distinguishes this sense of the term?).

Notions of parthood are ubiquitous. While sometimes conflated, there are clear distinctions which can be made between different types of parthood. The mereology pattern focuses on identifying these differences and making them explicit. The distinction between types of parthood may be best explained with the use of examples. An item may be contained in a car, but that does not make it a component of a car. For example, there may be a need to describe passengers or cargo being contained in a vehicle, but this relation needs to be distinguished from the parts and components that make up a vehicle. Similarly, the front of a car is intuitively a part of the car, but not a component of the car. While components of a vehicle may be defined, different city zone systems (wards, postal codes) are not components, but proper parts of larger areas.

Key Concepts and Classes

They key properties are formalized in Table 16. The Mereology pattern identifies the following different types of parthood: proper-part-of, component-of, and contained-in. A more detailed analysis, presented in Reference [19] reveals clear, ontological distinctions between each of these relations that may formalized clearly with a set of first-order logic axioms. The different properties may be described as follows: — partOf: specifies a part-whole relationship between objects — properPartOf: specifies a part-whole relationship between objects where an object cannot be part of itself — componentOf: specifies a part-whole relationship between objects where the part is defined based on actual boundaries. The parts are often also defined according to distinct functions. For example, a trunk is a componentOf a car. — immediateComponentOf: specifies a componentOf relationship where the if x immediateComponentOf y, then there does not exist a z where x immediateComponentOf z immediateComponentOf y. — containedIn: specifies a relationship between objects where one is not part (i.e. it is physically distinct) but instead is physically enclosed by the other (partially or wholly). For example, a suitcase is containedIn the trunk of a car. — immediateContainedIn: specifies a containedIn relationship where the if x immediateContainedIn y, then there does not exist a z where x immediateContainedIn z immediateContainedIn y. The aforementioned analysis (presented in Reference [19]) also identifies the expressive limitations of OWL, which prevent a complete representation of this semantics, and discussed the various possible approximations. It is important to consider what should be captured, and what distinctions should be made in the introduction of properties, in contrast with what is actually expressible in the logic. Since the required semantics cannot be completely captured in OWL, some trade-off(s) is required for any partial specification, (e.g. OWL only allows the specification of transitivity for simple object properties). The difficulty with such an approximation is that the resulting theory defines a semantics for something else entirely. Inherently, some semantics are omitted, which can potentially not be required for one application but can potentially be important for another. For example, if transitivity is a key aspect of some required reasoning, then perhaps a parthood relation would be defined as transitive, and some omissions would be made with respect to the formalization of other restrictions (e.g. cardinality) that should be applied to the parthood relation. Certainly, the use of approximations will be required in some cases, for example in order to support some desired reasoning problems. However, precisely which axiomatization is most suitable will vary between different usage scenarios. The Mereology Pattern therefore omits a detailed, partial axiomatization in favour of an under-axiomatized specification of the key relations, in order to avoid prescribing one trade-off over another. This leaves the commitment open-ended and variable to suit individual applications’ needs. This ontology defines the general properties such that the commonality between domain-specific part-of relations may be captured, and more detailed semantics may be defined in extensions of the properties. This creates a means of indicating the intended semantics of a relation by identifying the type of parthood that it is intended to capture, while allowing for the specification of different partial approximations of the semantics (and possibly also specializations of this semantics), as required. For example, a notion of parthood arises in the description of a building and the units it is divided into. In this case, this relationship can be identified as a sort of hasComponent relation; a new property hasBuildingUnit can be identified then as a subPropertyOf hasComponent. The most suitable approximation of the component-of relation can then be defined for the hasBuildingUnit relation. The approximation chosen for one type of parthood relation does not constrain the choice of approximation for another.

Status

Pending Approval

Supplementary Figures

Figure	Caption
	Mereology Pattern Example