The nature of the question: I have been thinking about a certain
mathematical system, and I am curious to know whether it has been
studied before and what might be said about it.
Specifically, I'm considering sets of Things, some of which may be
Triples (A, B, C) where A, B, and C are Things. You could think of
this is a specific family of directed labeled graphs (V, E) where e in
E implies e in V. However, it seems more geometrically intuitive to
think of Triples as triangles, but allow any triangle to have any
vertex be a triangle. Sort of like a simplicial complex, but with
recursion.
I'm interested in applying these systems to build semantic models
e.g. with triples like (cat, is a, mammal), (cat, eats, mice).
However, I want to be sure to understand the system thoroughly on
formal terms first. Including, how "expressive" is the system?
Other than than -- I'm interested in mathematical logic but haven't
studied it formally, so I thought I would ask you a few questions
about your course...
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