What algorithms exist for this hypergraph data structure?

This is very minimal, but it hints at a type of ontology structure and software system I want to develop. Does it remind you of any known, studied data structures and algorithms?

ontology = set()

def add(s):
  ontology.add(s)

def show():
  for item in ontology:
    print(item)

def link(s1, s2):
  # Python requires you add hashable objects to sets to determine duplicates; sets aren’t hashable because mutable, apparently
  ontology.add(frozenset([s1, s2]))

def delete(s):
  ontology.discard(s)

ontology = set()

def add(s):
  ontology.add(s)

def show():
  for item in ontology:
    print(item)

def link(s1, s2):
  # Python requires you add hashable objects to sets to determine duplicates; sets aren’t hashable because mutable, apparently
  ontology.add(frozenset([s1, s2]))

def delete(s):
  ontology.discard(s)

ontology = set()

def add(s):
  ontology.add(s)

def show():
  for item in ontology:
    print(item)

def link(s1, s2):
  # Python requires you add hashable objects to sets to determine duplicates; sets aren’t hashable because mutable, apparently
  ontology.add(frozenset([s1, s2]))

def delete(s):
  ontology.discard(s)

ontology = set()

def add(s):
  ontology.add(s)

def show():
  for item in ontology:
    print(item)

def link(s1, s2):
  # Python requires you add hashable objects to sets to determine duplicates; sets aren’t hashable because mutable, apparently
  ontology.add(frozenset([s1, s2]))

def delete(s):
  ontology.discard(s)

The key thing is this allows reification. You can add two things, link them, and that linked unit acts as a thing. You can link it to other things. Every link is a hyperedge. Every hyperedge is a node. It’s basically a subset of a set of elements closed under pairing.

One would want to develop more useful algorithms, at this point.

For starters:

An algorithm that checks that every element in every linked pair is present in the set.
An algorithm that finds all the elements linked with the same element.
An algorithm that combines every element linked to an element into a single element linked to that element.

The latter is partially a way to establish “definitions as extensions”: if we associate “animal” with “duck”, “animal” with “lion”, etc., we can merge all the animals into a single set of animals, and link it to the word “animal”.

Do you recognize this exact structure? Know any papers on it?

What algorithms exist for this hypergraph data structure?

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