this paper might be of help:
"Towards a Reference Terminology for Ontology Research and Development
in the Biomedical Domain"
http://ontology.buffalo.edu/bfo/Terminology_for_Ontologies.pdf
Erick
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Hi,
Below are some assumptions, followed by two questions.1. Categories are high level generic concepts e.g. Region
2. Universals are classes of actual things and particulars e.g. Country
3 Particulars are individual occurrences of universals e.g. Ireland
4. Categories are organized using subsumption hierarchies
(mathematically a sub-set relation).
5. Universals are organized using subsumption hierarchies
6. Individuals are elements of sets (mathematically element-of or set-membership relation)
Question 1: Are these assumptions correct?
Question 2: Is the relationship between Categories and Universals also
a subsumption relation, with the caveat the categories are higher up the hierarchy than universals?
6. Individuals are elements of sets (mathematically element-of or set-membership relation)Everything can be an element of a set, including a universal.
What I am trying to establish with point 6 is the nature of the hierarchy.
Is it the case that at the bottom of the hierarchy there is a switch from the subset relation to the element relation? This could be expressed as follows:
[6a] aParticular is-element-of aUniversal is-subset-of aCategory
If the universal Dog is a subset of the category Animal then the particular Fido is an element of Animal. Whereas, if I assume that Dog is an element of Animal, then I do not think that I can say that Fido is an element of Animal (because the element relation is non-compositional).
Is [6a] the correct interpretation of the hierarchy?
Regards,
Pat
On 25/07/11, Barry Smith <phis...@buffalo.edu> wrote:6. Individuals are elements of sets (mathematically element-of or set-membership relation)Everything can be an element of a set, including a universal.
What I am trying to establish with point 6 is the nature of the hierarchy.Is it the case that at the bottom of the hierarchy there is a switch from the subset relation to the element relation? This could be expressed as follows:[6a] aParticular is-element-of aUniversal is-subset-of aCategoryIf the universal Dog is a subset of the category Animal then the particular Fido is an element of Animal. Whereas, if I assume that Dog is an element of Animal, then I do not think that I can say that Fido is an element of Animal (because the element relation is non-compositional).Is [6a] the correct interpretation of the hierarchy?
Regards,Pat