I should add ... On 25 June 2013 12:01, Piaget Modeler <[email protected]> wrote: > >> Thanks Linas, for that. (I think.) >> >
Thanks for the compliment! Really, I do appreciate it. But my email box is utterly out of control, I have a few dozen unread emails marked as 'important', people are getting miffed that I haven't done stuff yet, and I'm going crazy working evenings and weekends. -- Linas > >> What do you know about Monads? And how do Monads differ from Atoms? >> > > > Sorry for the late reply. For some reason, these emails are going > straight into a folder, an not my inbox. > > I know of only three 'monads': that of Leibniz, the one that you mention, > and the concept from category theory. I understand the last one the best; > its basically a way of taking something, wrapping it and later unwrapping > it. I could kill some time trying to explain it in simple terms, but I'm > not sure what the point would be, as the general idea is useless if you > don't understand the category theoretical need to wrap and unwrap something > in the first place. > > -- Linas > >> >> >> >> >> Hi, >> >> On 21 June 2013 23:17, Piaget Modeler <[email protected]> wrote: >> >> >> Only difference is what the fundamental memory elements are (Atoms >> versus Monads) >> >> >> OpenCog Atoms might seem strange and artificial if you don't come from a >> mathematical background; they are, in fact, a probabilistic tweak to >> well-established formalisms for talking about structures of things. So, >> for example: >> >> If I look at your own charts at http://piagetmodeler.tumblr.com/ I see >> boxes connected by lines -- i.e. graphs, in the sense of "graph theory". >> Its worth reviewing the wikipedia article for that if you've never done >> so. Certain kinds of graphs, drawn with arrows, and having certain other >> properties, are categories, and are the subject of study in a rather >> abstract branch of mathematics called "category theory". If you ask what >> happens when you map one category to another (one graph to another) you >> find that they combine in only certain ways, something called "internal >> logic". The best-known of these is "intuitionistic logic", which is a lot >> like classical logic, but is missing the law of the excluded middle. In >> short, "graphs" and "logic" are inter-tied with one another; the ways of >> manipulating transformations of a graph correspond to a logic. And I >> really do mean "logic" -- concepts from classical logic like "there exists" >> and "for all" become pi-types and sigma-types, and so on. Unfortunately, >> the idea of "logic" also gets dizzying -- you get "Kripke semantics" and >> "Martin-Lof" type stuff ... >> >> OpenCog Atoms also have types; this is a nod to "type theory", which is >> another foundational theory of math. Types are used in (most) programming >> languages. They fix certain problems that set theory has... OK, wandering >> afield. You might also want to read about "term rewriting", "model >> theory", "universal algebra" each of these uses words such as "atom", >> "predicate", etc. that correspond to opencog ideas. In short, the general >> opencog idea of an "atom" is not just something random that Ben dreamed up, >> but is a common, consensus term widely used by people working in computer >> science, logic, mathematics. >> >> What's different is that Ben added a probability and uncertainty to it. >> That makes it look more Bayesian-ish or neural-net-ish. As a result, you >> can map concepts from those areas onto the atomspace, if you wish. Given >> the wide popularity of Bayesian and neural-net-ish stuff in AI, you should >> wish to do this. >> >> The one thing I haven't wrapped my mind around yet is the notion of >> "truth value". In opencog, its probabilistic; in these other branches, its >> a certain object that comes from a "subobject classifier". (The subobject >> classifier for sets has truth values of 0,1 or true/false. Subobject >> classifiers for more general categories have a much wider range of truth >> values (sieves). Concepts from logic, such as "and", "or", "not", >> "for-each", "there-exists" likewise generalize to products, disjoint >> unions, etc. I haven't yet made the bridge between these, and Bayesian >> notions of the same.) >> >> Anyway, while developing this new thing, a "monad", you may find it >> profitable to draw inspiration from all these different fields -- you may >> find more commonality than you'd think; or that what's old is new again. >> >> -- Linas >> >> *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> >> <https://www.listbox.com/member/archive/rss/303/19999924-4a978ccc> | >> Modify <https://www.listbox.com/member/?&;> Your Subscription >> <http://www.listbox.com> >> *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> >> <https://www.listbox.com/member/archive/rss/303/8350022-de8a4249> | >> Modify<https://www.listbox.com/member/?&;>Your Subscription >> <http://www.listbox.com> >> > > ------------------------------------------- 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
