Adding Edge Pattern and Relation Types

[callahantiff]

New Edge Metadata

I am hoping to add two types of relation-specific metadata to the statistics that are currently generated with each KG build: (i) relation types and (ii) relation patterns. A brief description of each is included below. The thing to keep in mind when considering how we might generate these stats is that we need strategies for generating them for our OWL builds and the OWL-NETS builds.

Relation Types

Resources: arXiv paper

I think it's most useful to think of these things in terms of tail and relation pairs versus a head node or head and relation pairs versus a tail node.

1. 1:1: only one tail node points only one other type of tail node
2. 1:N: one head node points to at least one tail node (e.g., one variant can contribute to multiple phenotypes)
3. N:1: more than one head node points to the same tail node (e.g., many proteins have the same cellular location)
4. N:N: more than one head node is connected to more than one tail node (e.g., many proteins interact with many other proteins)

I also attempted to draw the silly picture included below.

Relation Patterns

Resources: Stanford Lecture; article, page 27

1. Symmetric: r ∈ R is symmetric if ∀(h, r, t) ∈ G, (t, r, h) ∈ G (e.g., moleculary interacts)
2. Antisymmetric: r ∈ R is anti-symmetric if ∀(h, r, t) ∈ G, (t, r, h) ∉ G
3. Inversion: r ∈ R then the inverse R^-1 = {∀(h, r, t) : (t, r, h) ∈ R}
4. Transitive): r ∈ R is transitive if ∀ pairs of facts (h, r, x) ∈ G and (x, r, t) ∈ G, (h, r, t) ∈ G as well (for OWL KGs this is easily identified easily through owl:TransitiveProperty)
5. Reflexive: r ∈ R is reflexive if ∀(h, r, t) ∈ G, (h, r, h) ∈ G
6. Irreflexive: r ∈ R is irreflexive if ∀e ∈ ɛ(e, r, r) ∉ G

Notes

• I think I have a good sense of how to find the first three in both OWL and OWL-NETS, but patterns 4-6 seem to be a bit tricker. Perhaps we might be able to discuss some heuristics for these?
• We will have to make sure we have the math solid since some theorem state if a relation is one of these things it's also another.

Other relevant or Linked Issues: #99

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@bill-baumgartner - Can you please confirm if you agree with this? Any help or insight you have would also be greatly appreciated! 😄

[sanyabt]

Hi @callahantiff, dropping in for a quick comment that Scott Malec (@kingfish777) mapped relations in the Relation Ontology to the above relation patterns for our symmetric and transitive closure on literature-based knowledge and semantic relation extraction graph last year. Will be happy to share that if it is useful 😄

[callahantiff]

Hi @callahantiff, dropping in for a quick comment that Scott Malec (@kingfish777) mapped relations in the Relation Ontology to the above relation patterns for our symmetric and transitive closure on literature-based knowledge and semantic relation extraction graph last year. Will be happy to share that if it is useful 😄

Oh, yes, please! That would be awesome! Thank you so much for sharing!

[sanyabt]

Of course! I am meeting him tomorrow and will make sure I have the latest version then share it with you.