I believe my response to Hawkins' book, written in 2004, still holds as a response to Kurzweil's book (with its similar theme) as well:
http://www.goertzel.org/dynapsyc/2004/OnBiologicalAndDigitalIntelligence.htm -- Ben Goertzel On Mon, Nov 19, 2012 at 4:42 PM, Micah Blumberg <[email protected]> wrote: > YKY your approach does not personally make sense to me. Naturally I hope > you are successful. Have you read either "On Intelligence" by Jeff Hawkins > or "How to create a mind" by Ray Kurzweil. The latter book was recently > published. I suspect that many people trying to build AGI will be able to > consider a new approach to after reading it. Please let me know if you are > aware of that kind of AI and what advantages your planned system may have > over it. > > > On Sun, Nov 18, 2012 at 9:20 PM, Aaron Hosford <[email protected]>wrote: > >> My matrix representation is based on the observation that AB != BA in the >>> composition of concepts, for example "john loves mary != mary loves john". >>> I'm still trying to determine if the matrix representation is sound and >>> consistent with our common-sense view of concepts, but it looks promising... >> >> >> I may be jumping to conclusions, but it sounds like what you're doing is >> placing A/"john", B/"mary", etc. as labels for both rows and columns, where >> the row label represent the first value and the column represents the >> second (or maybe vice versa), so that you can represent "john loves mary" >> by placing a nonzero value in entry indexed by row "john" and column >> "mary". The most obvious interpretation for this nonzero value would be the >> probability that "john loves mary" is true, or it could possibly be >> certainty or some other similar measure. >> >> As you pointed out, this is a nice generalization of a basic adjacency >> matrix, with nonzero entries marking adjacencies (directed links or edges) >> in the conceptual graph. Matrices of this form could be mapped to directed >> graphs with links not only labeled "loves", but having a secondary label >> indicating the associated probability or certainty value of the link. In my >> own system, I keep my internal representation directly in terms of nodes & >> links rather than such a generalized adjacency matrix, but the specific >> data structure is really only an implementation detail, not intrinsic to >> the structure of the information being stored. We are basically doing the >> same thing, in other words, provided my understanding of your >> representational method is correct. >> >> I'm still trying to determine if the matrix representation is sound and >>> consistent with our common-sense view of concepts, but it looks promising... >> >> >> I have spent a lot of time thinking about this problem, albeit in terms >> of semantic nets rather than the matrices that correspond to them. I think >> your approach is consistent with how we internally work with concepts, but >> it is probably incomplete. For example, what happens when you want to >> represent the probability or certainty that "john" is the one participating >> as the subject in this "loves" relationship independently from the >> probability/certainty that "mary" is the direct object? Or what if you have >> lower probability/certainty for the classification of the relationship as >> "loves" (as opposed to say, "hates") than you do for the individuals >> filling the subject and direct object roles? It seems now that you need 3 >> probability/certainty numbers for each position in the matrix, one for >> subject, one for direct object, and one for relationship type. >> >> Instead of multiple values in a single cell of the matrix -- or rather 3 >> parallel matrices with the same row and column labels -- it seems more >> natural to me to make the clause/predicate/act/relationship a separate >> value in itself, so the original matrix is decomposed into (1) a "subject" >> matrix, mapping the probability/certainty of "john" (among other people) >> participating in the clause as the subject, (2) a "direct object" matrix, >> mapping the probability/certainty of "mary" (among other people) >> participating in the clause as the direct object, and (3) a "predicate" >> matrix, mapping the probability/certainty that the clause's predicate is >> "loves" (among other possible predicates). Each of these different >> matrices, "subject", "direct object", and "predicate", maps to a link label >> in the corresponding directed graph, and each link receives its own >> probability/certainty value independent of the others. The representational >> advantage of making the clause itself a row/column label only grows when >> prepositional phrases, adverbs, indirect objects, and other clausal >> modifiers start to come into play, and the utility of your matrix trick is >> preserved by simply adding a new matrix for each constituent role in the >> clause. >> >> >> >> On Sun, Nov 18, 2012 at 8:10 PM, YKY (Yan King Yin, 甄景贤) < >> [email protected]> wrote: >> >>> On Sat, Nov 10, 2012 at 3:44 AM, Aaron Hosford <[email protected]>wrote: >>> >>>> My "matrix trick" may be able to map propositions to a high-dimensional >>>>> vector space, but my assumption that concepts are matrices (that are also >>>>> rotations in space) may be unjustified. I need to find a set of criteria >>>>> for matrices to represent concepts faithfully. This direction is still >>>>> hopeful. >>>> >>>> >>>> I'm curious what your "matrix trick" is. Are you familiar with >>>> adjacency matrices? They're the simplest and most common way of >>>> representing directed graphs as matrices. >>>> http://en.wikipedia.org/wiki/Adjacency_matrix Semantic nets typically >>>> have sparse adjacency matrices, and there are a lot of good algorithms and >>>> libraries out there for efficiently representing and manipulating sparse >>>> matrices. >>>> >>> >>> >>> Sorry, almost missed your post. My method is to *represent* logical >>> atoms as square matrices with real entries. This allows me to convert the >>> matrices to vectors (by simply flattening the matrices) and calculate the >>> distances (ie similarities) between them via the Euclidean norm. >>> >>> My matrices are different from adjacency matrices which has integer >>> entries. The continuous values potentially allow learning via propagation >>> of errors similar to back-propagation for neural nets. >>> >>> My matrix representation is based on the observation that AB != BA in >>> the composition of concepts, for example "john loves mary != mary loves >>> john". I'm still trying to determine if the matrix representation is sound >>> and consistent with our common-sense view of concepts, but it looks >>> promising... >>> >>> YKY >>> *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> >>> <https://www.listbox.com/member/archive/rss/303/23050605-bcb45fb4> | >>> 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/303/23601407-ccf7ca1d> | >> Modify <https://www.listbox.com/member/?&;> Your Subscription >> <http://www.listbox.com> >> > > > > -- > > ~~ > Warmly, > > > Micah > 7 1 4 ) 6 9 9 - 4 2 1 3 (voicemail and texting same digits) > *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/212726-c2d57280> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <http://www.listbox.com> > -- Ben Goertzel, PhD http://goertzel.org "My humanity is a constant self-overcoming" -- Friedrich Nietzsche ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-c97d2393 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-2484a968 Powered by Listbox: http://www.listbox.com
