How can I represent that a class relates to an instance in terms of an ontology?

Question

I want to use mathematical or knowledge representation notation to say that if a class relates to an instanse then there is a relationship or something like that.

you have an ontology with classes and instances. I want to show that a class is related to an instance but not in a child-parent relationship. I want to represent this in a formal mathematical way with symbols. Thanx

Answer 1

The question is not clear, but you might want to look into a branch of mathematics known as category theory.

Update:
OK, now I get it. You are talking about ontology in the computer science sense. This is an interesting question. I will come back if I can see a way to describe this with mathematical terminology.

Essentially, it sounds like you want a symbolic, mathematical way to encode one of the ontology languages. Those languages let you form relationchips between classes and instances.

It appears to me that there should be a way to do this using a branch of math knows as graph theory. I'll update if I get more.

Further update:

This article talks in general terms about using the mathematics of category theory in work on ontologies.
http://www.aifb.uni-karlsruhe.de/WBS/phi/pub/pos_catmerge.pdf

These postings suggests that in general situations, we may need to use the more general theory of hypergraphs, rahter than traditional graph theory, for ontologies.

http://suo.ieee.org/email/msg02653.html
http://suo.ieee.org/email/msg02653.html

Last Update:

The best I can come up with is to suggest that you do this with hypergraphs. That way, you can avoid having to place restrictions on the number of relations you can have between a calss and an instance. And hypergraphs are normally done with mathematical notation, as opposed to pictorial graphs. Unfortunately, I do not know enough graph theory to complete the problem for you. To get started, look here:

http://en.wikipedia.org/wiki/Hypergraph

Thanks for posting such an interesting question!


To English I

Oh yes, category theory and graph theory are very much subfields of math! You can do a Phd in either subject in many math departments worldwide. Ontology may come from computer science, but representing it in mathematical terms is a mathematics problem.

Answer 2

I suggest you be a bit more specific and also address this question to the philosophy interest group.

Answer 3

Thats not math.