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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?

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A formalism of the data is based on the notion of the extended directed graph is developed. Operations and data structure classes are defined. Properties of data structures are studied; in particular, the definition of a data structure by means of its operations is investigated.

You can refer the following link for the better understanding:

https://link.springer.com/article/10.1007%2FBF00276183

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.

Learn Data Structures with the help of this Data Structures with Python Cheat Sheet.

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