Is there a formalism for this data structure?

Question

I'm looking for a mathematical formalism for a data structure I'm working with, so that I can track down relevant theorems and algorithms.

Suppose you have the following:

• A directed acyclic graph of topics.
• At each topic, there are one or more relations between the topic, items in a set of documents and items in a set of groups.
• The groups may be a simple set or they may end up as a DAG. They are used to manage the visibility of the association of a document with a topic.

Only recently have I come across hypergraphs, which seem relevant but too general. Is there a formalism for this data structure? If not, can it be described more succinctly in mathematical terms?

Answer 1

This looks like http://en.wikipedia.org/wiki/Formal_concept_analysis , especially Galois lattice.

A lattice has more constraints than what you describe, but maybe you can adopt this formalism in your application, or start from here to see if there are related works closer to your needs.

I guess you already know http://en.wikipedia.org/wiki/Ontology_%28information_science%29 , which is also the starting point of a lot of resources.