Hi,
On 25 June 2013 12:01, Piaget Modeler <[email protected]> wrote: > Thanks Linas, for that. (I think.) > > 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
