Trivial Geometry Ontology

This ontology is created out of the need for an Ellipse and Point. During the construction of a gel ontology (CC2GO), I am forced to create certain geometric concepts in order to write meaningful application. But I am by no means an expert on Geometry. Even if I am, I do not intend to build a full fledged Geometry ontology because we are in the field of proteomics - not mathematics. Hence, we have to adopt a relative pragmatic approach. To separate these concepts in a separate ontology allow us or others to change to a more authoritive (or popular) definition in the future.

The basic concepts are defined in the following figure.

Figure 1 Trivial Geometry Ontology denoted in DLG²

It is not difficult to see that most concepts are simple geometric concepts. It is worth to note, all these concepts are assummed to be on a two-dimensional plane. It is not guaranteed that the assumed 2D-planes are the same from two different discriptions are the same. Neither is the coordinate system and unit of all data type values. All these contextual information should be made clear from the RDF document who uses these concepts.

Classes

Point

Conceptualization

I will not make a strict definition for the point. But in here, a point refers to a location on a user-defined (or assumed) Cartesian plane that has an implicit (again, user defined) coordinate systems.

Axioms

Obviously, a point on a 2D place shall carry two attribute x and y.

Ellipse

Conceptualization

Ellipse is a rdfs:subClass of "Shape" that is a circle but stretched at one direction. The major and minor axises of a ccbase:Ellipse shall be parallel to the coordinates of the implicit user defined coordinate system (See Figure 2).

Figure 2 The definition of a ccbase:Ellipse

Axioms

Obviously, an Ellipse shape can be defined with a rx and ry.

Properties

x

A tvo:x is a owl:Datatype property that has a domain of ccbase:Point.

y

A tvo:y is a owl:Datatype property that has a domain of ccbase:Point.

rx

A tvo:rx is a owl:Datatype property that has a rdfs:domain of ccbase:Ellipse. It refers to the radius that is parallel to the x-axis of the assumed coordinate system. (see figure 2)

ry

A tvo:ry is a owl:Datatype property that has a rdfs:domain of ccbase:Ellipse. It refers to the radius that is parallel to the y-axis of the assumed coordinate system. (see Figure 2)

The definition of this ontology is "http://www.charlestoncore.org/ontology/2005/08/geometry#"