GFO Part I Basic Principles
 Ontological Investigations Conceptual Modelling Onto-Builder Axiomatic Foundations Domain Ontologies Onco-Workstation Metalogical Analyses Ontology Languages SOP-Creator

Subsections

## 14.5 Parthood Relation

Part-of is a basic relation between certain kinds of entities, and several relations have a similar character.

### 14.5.1 Abstract and Domain-specific Part-of Relations

The abstract part-of relation is denoted by , while the argument-types of this relation are not specified, i.e., we allow arbitrary entities to be arguments. We assume that satisfies the condition of a partial ordering, i.e., the following axioms:

, , and .

Domain-specific part-of-relations are related to a particular domain , which might be the set of instances of a category. We denote these relations as . We assume that for a domain , the entities of and its parts are determined. There is a large family of domain-specific part-of relations, the most general of these are related to basic categories as , , , , , . In the following sections we provide an overview of the most important category-specific part-of relations.

### 14.5.2 Part-of Relation for Sets

We hold that the part-of-relation of sets is defined by the set inclusion, hence . If we assume the power-set axiom for sets, then the mereology of sets corresponds to the theory of Boolean algebras.

### 14.5.3 Part-of-Relations for Time and Space

The part-of relations of time and space are related to chronoids, time-regions, topoids, and space regions. We introduce the unary predicates , , , , and the binary relations , .

Every notion of part-of allows for a non-reflexive version of the relationship, which expresses proper parthood. These are denoted by adding a p'' to the above predicates, e.g. or .

In particular, applies to spatial regions, refers to time regions and chronoids, while represents a relationship between situoids (or situations) and their constituents. The constituents of a situoid include, among other entities, the pertinent material structures (that participate in ) and the qualities that inhere in them. Further, facts and configurations are constituents of situoids. Not every part of a constituent of a situoid, however, is contained in it.

### 14.5.4 Part-of Relation for Material Structures

The basic relations pertaining to material structures are , for  is a material structure'', and , which means that the material structure is a part of the material structure . We assume among the basic axioms:

We stipulate that the relation is a partial ordering, but additional axioms depend strongly on the domain under consideration.

### 14.5.5 Part-of-Relation for Processes

The part-of relation between processes is denoted by , meaning that the process is a processual part of the process . We assume the basic axiom:

.

states that the process has the temporal extension , or that the process is temporally projected onto .

Again, we stipulate that the relation is a partial ordering, but additional properties of this relation depend on a concrete domain. For example, in the processes of surgery, only certain processual parts are relevant.

### 14.5.6 Role-of

The role-of relationship was introduced as a close relative of part-of. It relates roles and their contexts , denoted by . Thus far we have introduced role-of between processual roles and processes and between relational roles and relators.

Robert Hoehndorf 2006-10-18