You are welcome. I have learned a lot of basics of hypergraph from your message, thanks.
BTW, now I suspect there is some interesting relation between Hypergraph and F-(co)algebra.
For example, a DG G = [x-[x,y], y-[x-z], z-[]] is a funtion from a domain of nodes D={x,y,z} into pow(D): the powerset of the nodes {x,y,z}. G: D -> pow(D). Computer scientists/logicians call G a pow-coalgebra over D.
Once I saw much works under title “coalgebraic logics”. It was too difficult for me to catch up with. But I will be very glad if you are interested in hypergraph and coalgebraic logics and get something interesting there.
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Since I am Datalog biased, here my question. Did this deliver some
results in non-monotonic updates and/or programs with negation?
Or is it rather useless so that it can be ignored?
I saw a theorem on a mixed fixpoint of mixed systems consisting of mutually dependent coalgebras and algebras which may be related to your question. But it had gone out of my poor memory a long time ago, though I believe there has been a lot of researches on these mixed fixpoints.
You nowhere say what mixed fixpoints are. A google search
tells me that they are not very novel, this paper is from 1997,
also they don’t work with co-algebras:
https://www.researchgate.net/publication/2720205
More worse, F-coalgebra and F-algebras are discussed
with the assumption F being monotone. ( e.g. pow is monotone). Negation may violate the monotonicity assumption. It is better for you to forget my noisy comment.