Our mereological ontology is simply an Ontolingua implementation of the Classical Extensional Mereology as described in [Simons, 1987]. We therefore only give a brief explanation of this ontology and refer to [Simons, 1987] for the details and more philosophical aspects. Two relations define part-of decompositions. The relation equal(x,y) defines which individuals are to be considered mereologically equal. In the usual case, it only holds for equal(x,x) but in some situations it is convenient to say that two individuals are equal when they have the same parts. An individual x is a mereological individual when equal(x,x) holds. When a mereological individual x is a part of a mereological individual y, the relation proper-part-of(x,y) holds. With these relations it is possible to write down a variety of axioms specifying desirable properties any system decomposition should have. Examples are the asymmetry and transitivity of the proper-part-of relation.
Figure 3:
Excerpt from the mereological ontology. This ontology defines the
means to specify decomposition information and the properties any
decomposition should have.
Figure 3 shows an excerpt from the mereological ontology. Definition 2 defines the class of mereological individuals that was sketched above. The definition of the proper-part-of relation clearly shows the asymmetry (3a) and transitivity (3b) axioms. Note that these definitions only serve as an illustration and are not meant to be complete. The ontology furthermore defines the relation disjoint(x,y) which holds for individuals that do not share a part and simple-m-individual, the class of individuals that have no decomposition.