YKY, As we use it in OpenCog, our weighted/labeled hypergraph is not really best thought of as equivalent to a set of propositions... It's more flexible than that -- some parts of it are more like predicate calculus, some are more like probabilistic grammars, etc.
As for simplicial complexes, the complexity (sorry ;p) of the mapping from hypergraphs to simplicial complexes comes when you move from topology to geometry. Topologically the mapping is clear. Geometrically it's not clear to me at the moment, because the area of the face of a simplicial complex (as one would normally compute it) seems to have no obvious useful interpretation in terms of the semantics of the hyper-edge that is the boundary of the face.... Unless one does something new/strange, which I haven't figured out yet (but bear in mind, this is just some amusing background-thinking I'm doing, not really needed for the main stream of OpenCog development... I just like to keep the creative thinking going...) ben On Sun, Mar 19, 2017 at 11:56 PM, YKY (Yan King Yin, ηζ―θ΄€) < [email protected]> wrote: > Thanks for telling me that hypergraphs are simplicial complexes... > > I reckon hypergraphs can be broken down as a list of subsets (from the > powerset of nodes). This could also be viewed as a list of propositions, 1 > proposition = 1 hyper-edge. > > So, the hypergraph representation is pretty much equivalent to a set of > propositions. > > In my new theory I'm still using the set-of-propositions as knowledge > representation, albeit the propositions are mapped to vector space, such > that they can be acted on by a deep neural net. > > I'm wondering if the hypergraph β simplicial complex idea could lead to a > drastically different kind of representation structure, unlike the > set-of-proposition ones? > > 2) Even if you have probability distributions over the hypergraphs, that > doesn't give you much leverage. The bottleneck of AGI is in the learning > algorithm... I think we should focus on how to make *that* faster π > > YKY > *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/19237892-5029d625> | > Modify > <https://www.listbox.com/member/?&;> > Your Subscription <http://www.listbox.com> > -- Ben Goertzel, PhD http://goertzel.org βOur first mothers and fathers β¦ were endowed with intelligence; they saw and instantly they could see far β¦ they succeeded in knowing all that there is in the world. When they looked, instantly they saw all around them, and they contemplated in turn the arch of heaven and the round face of the earth. β¦ Great was their wisdom β¦. They were able to know all.... But the Creator and the Maker did not hear this with pleasure. β¦ βAre they not by nature simple creatures of our making? Must they also be gods? β¦ What if they do not reproduce and multiply?β Then the Heart of Heaven blew mist into their eyes, which clouded their sight as when a mirror is breathed upon. Their eyes were covered and they could see only what was close, only that was clear to them.β β Popol Vuh (holy book of the ancient Mayas) ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-f452e424 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-58d57657 Powered by Listbox: http://www.listbox.com
