GFO Part I Basic Principles



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			Onto-Med >> Theories >> GFO Part I Basic Principles
			Overview General Formal Ontology (GFO)	Next: 14.6 Boundaries, Coincidence, and Up: 14 Ontologically Basic Relations Previous: 14.4 Property Relations Subsections 14.5.1 Abstract and Domain-specific Part-of Relations 14.5.2 Part-of Relation for Sets 14.5.3 Part-of-Relations for Time and Space 14.5.4 Part-of Relation for Material Structures 14.5.5 Part-of-Relation for Processes 14.5.6 Role-of 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 $\Gp(x,y)$ , while the argument-types of this relation are not specified, i.e., we allow arbitrary entities to be arguments. We assume that $\Gp(x,y)$ satisfies the condition of a partial ordering, i.e., the following axioms: $\Gp(x,x)$ , $\Gp(x,y) \wedge \Gp(y,x) \rightarrow x = y$ , and $\Gp(x,y) \wedge \Gp(y,z) \rightarrow \Gp(x,z)$ . 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 $\Gpart_{D}(x,y)$ . 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 $\GChron(x)$ , $\GTReg(x)$ , $\GTop(x)$ , $\GSReg(x)$ , $\GMatS(x)$ , $\GProc(x)$ . 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 $\Gpart_{S} (x,y) =_{df} \GSet(x) \wedge \GSet(y) \wedge x \subseteq y$ . 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 $\GChron(x)$ , $\GTReg(x)$ , $\GTop(x)$ , $\GSReg(x)$ , and the binary relations $\Gtpart(x,y)$ , $\Gspart(x,y)$ . 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. $\Gpp(x,y)$ or $\Gtppart(x,y)$ . In particular, $\Gspart$ applies to spatial regions, $\Gtpart$ refers to time regions and chronoids, while $\Gcpart$ 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 $\GMatS(x)$ , for `` is a material structure'', and $\Gmatpart(x,y)$ , which means that the material structure is a part of the material structure . We assume among the basic axioms: $\forall x y u v (\GMatS(x) \wedge \Gmatpart(y,x) \wedge \Gocc(x,u) \wedge \Gocc(y,v) \rightarrow \Gspart(v,u))$ We stipulate that the relation $\Gmatpart(x,y)$ 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 $\Gprocpart(x, y)$ , meaning that the process is a processual part of the process . We assume the basic axiom: $\forall x y (\GProc(x) \wedge \Gprocpart (y,x) \wedge \Gprt(x,u) \wedge \Gprt(y,v) \rightarrow \Gtpart(v,u)$ . $\Gprt(x,u)$ states that the process has the temporal extension , or that the process is temporally projected onto . Again, we stipulate that the relation $\Gprocpart(x, y)$ 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 $\Groleof(x,y)$ . Thus far we have introduced role-of between processual roles and processes and between relational roles and relators. Next: 14.6 Boundaries, Coincidence, and Up: 14 Ontologically Basic Relations Previous: 14.4 Property Relations Robert Hoehndorf 2006-10-18