On Sun, Oct 8, 2017 at 1:42 PM, Amirouche Boubekki < amirouche.boube...@gmail.com> wrote:
> > > On Sat, Oct 7, 2017 at 4:12 PM Linas Vepstas <linasveps...@gmail.com> > wrote: > > >> For the last ten years, I've been thinking of the atomspace as a "graph >> database". In the last 6+ months, I'm starting to realize that this is the >> wrong viewpoint. I think I know a better one, but it takes some explaining. >> > > What is your new viewpoint? > This one: https://github.com/opencog/atomspace/tree/master/opencog/sheaf I quote: ... a simple and convenient mechanism for working with graphs "locally", by making the nearest-neighbors of a vertex apparent. The traditional textbook-canonical way of specifying a graph is to state that it is a set of vertexes, and a set of edges that connect pairs of vertexes. The problem with this description is that given any vertex, one has no idea of what edges are connected to it, without scanning the entire set of edges. Another problem is that vertexes and edges are not composable; that is, when they are composed together, they are no longer vertexes or edges, but a more general type: a "subgraph". By contrast, sheaves carry local information, and are composable. Given a vertex V, a "section" is defined as a set of pairs (V,E) of that vertex V and all edges E that are attached to it. That's it! Very simple! A section can be envisioned as a "spider", with the vertex V as the body of the spider, and the edges as the legs of the spider. Sections are composable, in that several can be connected together by joining ("connecting") edges. The result is still a section, in that it has a central blob as the spider-body, and a whole bunch of legs sticking out. Composing sections in such a way that the edges connect only in legal ways is called "parsing". Another way of visualizing sections is to envision a jigsaw-puzzle piece instead of a spider. The vertex V is a label on the puzzle-piece, and each leg is a tab or slot on the puzzle-piece. The tabs or slots are now obviously connectors: this emphasizes that jigsaw-puzzle pieces can be connected together legally only when the connectors fit together. Again: the act of fitting together puzzle-pieces in a legal fashion is termed "parsing". In standard mathematical terminology, the spider-body or jigsaw-label is called the "germ". It is meant to evoke the idea of a germinating seed, as will become clear below. Diagramatic illustrations of jig-saw puzzle-pieces can be found here: - Sleator, Temperley, Parsing English with a Link Grammar <http://www.cs.cmu.edu/afs/cs.cmu.edu/project/link/pub/www/papers/ps/tr91-196.pdf> - Bob Coeke, New Scientist: Quantum Links Let Computers Read <http://www.cs.ox.ac.uk/people/bob.coecke/NewScientist.pdf> --linas -- *"The problem is not that artificial intelligence will get too smart and take over the world," computer scientist Pedro Domingos writes, "the problem is that it's too stupid and already has." * -- You received this message because you are subscribed to the Google Groups "opencog" group. To unsubscribe from this group and stop receiving emails from it, send an email to opencog+unsubscr...@googlegroups.com. To post to this group, send email to opencog@googlegroups.com. Visit this group at https://groups.google.com/group/opencog. To view this discussion on the web visit https://groups.google.com/d/msgid/opencog/CAHrUA36MpPL1e_3TPq0k%2BBwrKwA%2B_w0oF45DczGSPxiXnmVEug%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
