Hi Ben, What's TTR?
We can talk about link-grammar, but I want to talk about something a little bit different: not PLN, but the *implementation* of PLN. This conversation requires resolving the "category error" email I sent, just before this. Thus, I take PLN as a given, including the formulas that PLN uses, and every possible example of *using* PLN that you could throw my way. I have no quibble about any of those examples, or with the formulas, or with anything like that. I have no objections to the design of the PLN rules of inference. What I want to talk about is how the PLN rules of inference are implemented in the block of C++ code in github. I also want to assume that the implementation is complete, and completely bug-free (even though its not, but lets assume it is.) Now, PLN consists of maybe a half-dozen or a dozen rules of inference. They have names like "modus ponens" but we could call them just "rule MP" ... or just "rule A", "rule B", etc... Suppose I start with some atomspace contents, and apply the PLN rule A. As a result of this application, we have a "possible world 1". If, instead, we started with the same original atomspace contents as before, but applied rule B, then we would get "possible world 2". It might also be the case that PLN rule A can be applied to some different atoms from the atomspace, in which case, we get "possible world 3". Each possible world consists of the triple (some subset of the atomspace, some PLN inference rule, the result of applying the PLN rule to the input). Please note that some of these possible worlds are invalid or empty: it might not be possible to apply the choosen PLN rule to the chosen subset of the atomspace. I guess we should call these "impossible worlds". You can say that their probability is exactly zero. Observe that the triple above is an arrow: the tail of the arrow is "some subset of the atomspace", the head of the arrow is "the result of applying PLN rule X", and the shaft of the arrow is given a name: its "rule X". (in fancy-pants, peacock language, the arrows are morphisms, and the slinging together, here, are kripke frames. But lets avoid the fancy language since its confusing things a lot, just right now.) Anyway -- considering this process, this clearly results in a very shallow tree, with the original atomspace as the root, and each branch of the tree corresponding to possible world. Note that each possible world is a new and different atomspace: The rules of the game here are that we are NOT allowed to dump the results of the PLN inference back into the original atomsapce. Instead, we MUST fork the atomspace. Thus, if we have N possible worlds, then we have N distinct atomspaces. (not counting the original, starting atomspace) Now, for each possible world, we can apply the above procedure again. Naively, this is a combinatoric explosion. For the most part, each different possible world will be different than the others. They will share a lot of atoms in common, but some will be different. Note, also, that *some* of these worlds will NOT be different, but will converge, or be "confluent", arriving at the same atomspace contents along different routes. So, although, naively, we have a highly branching tree, it should be clear that sometimes, some of the branches come back together again. I already pointed out that some of the worlds are "impossible" i.e. have a probability of zero. These can be discarded. But wait, there's more. Suppose that one of the possible worlds contains the statement "John Kennedy is alive" (with a very very high confidence) , while another one contains the statement "John Kennedy is dead" (with a very very high confidence). What I wish to claim is that, no matter what future PLN inferences might be made, these two worlds will never become confluent. There is also a different effect: during inferencing, one might find oneself in a situation where the atoms being added to the atomspace, at each inference step, have lower and lower probability. At some point, this suggests that one should just plain quit -- that particular branch is just not going anywhere. its a dead end. OK, that's it, I think, for the overview. Now for some commentary. First, (let get it out of the way now) the above describes *exactly* how link-grammar works. For "atomspace" substitute "linkage" and for "PLN rule of inference" substitute "disjunction". That's it. End of story(QED). Notice that each distinct linkage in link-grammar is a distinct possible-world. The result of parsing is to create a list of possible worlds (linkages, aka "parses"). Now, link-grammar has a "cost system" that assigns different probabilities (different costs) to each possible world: this is "parse ranking": some parses (linkages) are more likely than others. Note that each different parse is, in a sense, "not compatible" with every other parse. Two different parses may share common elements, but other parts will differ. Claim: the link-grammar is a closed monoidal category, where the words e the objects, and the disjuncts are the morphisms. I don't have the time or space to articulate this claim, so you'll have to take it on faith, or think it through, or compare it to other papers on categorial grammar e.g. the Bob Coecke paper op. cit. It is useful to think of link-grammar disjuncts as jigsaw-puzzle pieces, and the act f parsing as the act of assembling a jigsaw puzzle. (Se the original LG paper for a picture of the jigsaw pieces. The Coecke paper also draws them. So does the Baez "rosetta stone" paper, though not as firmly) Theorem: the act of applying PLN, as described above, is a closed monoidal category. Proof: A "PLN rule of inference" is, abstractly, exactly the same thing as a link-grammar disjunct. The contents of the atomspace is exactly the same thing as a (partially or fully) parsed sentence. QED. There is nothing more to this proof than that. I mean, it can fleshed it out in much greater detail, but that's the gist of it. Observe two very important things: (1) during the proof, I never once had to talk about modus ponens, or any of the other PLN inference rules. (2) during the proof, I never had to invoke the specific mathematical formulas that compute the TV's -- that compute the strength and confidence. Both of these aspects of PLN are completely and utterly irrelevant to the proof. The only thing that mattered is that PLN takes, as input, some atoms, and applies some transformation, and generates atoms. That's it. The above theorem is *why* I keep talking about possible worlds and kripke-blah-blah and intuitionistic logic, and linear logic. its got NOTHING TO DO WITH THE ACTUAL PLN RULES!!! the only thing that matters is that there are rules, that get applied in some way. The generic properties of linear logic and etc. are the generic properties of rule systems and kripke frames. Examples of such rule systems include link-grammar, PLN, NARS, classical logic, and many more. The details of the specific rule system do NOT alter the fundamental process of rule application aka "parsing" aka "reasoning" aka "natural deduction" aka "sequent calculus". Confusing the details of PLN with the act of parsing is a category error: the logic that describes parsing is not PLN, and PLN dos not describe parsing: its a category error to intermix the two. Phew. What remains to be done: I believe that what I describe above, the "many-worlds hypothesis" of reasoning, can be used to create a system that is far more efficient than the current PLN backward/forward chainer. It's not easy, though: the link-parser algorithm struggles with the combinatoric explosion, and has some deep, tricky techniques to beat it down. ECAN was invented to deal with the explosion in PLN. There are other ways. By the way: the act of merging the results of a PLN inference back into the original atomspace corresponds, in a very literal sense, to a "wave function collapse". As long as you keep around multiple atomspaces, each containing partial results, you have "many worlds", but every time you discard or merge some of these atomspaces back into one, its a "collapse". That includes some of the TV merge rules that plague the system. Next, I plan to convert this email into a blog post. --linas On Wed, Aug 31, 2016 at 1:05 AM, Ben Goertzel <[email protected]> wrote: > Regarding link parses and possible worlds... > > In the TTR paper they point out that "possible worlds" is somehow > conceptually misleading terminology, and it may often be better to > think about "possible situations" (in a deep sense each possible > situation is some distribution over possible worlds, but it may rarely > be necessary to go that far) > > In that sense, we can perhaps view the type of a link parse as a > dependent type, that depends upon the situation ... (?) > > This is basically the same as viewing the link-parser itself as a > function that takes (sentence, dictionary) pairs into functions that > map situations into sets of link-parse-links [but the latter is a > more boring and obvious way of saying it ;p] > > But again, I don't (yet) see why linear logic would be required > here... it seems to me something like TTR with <p,n> truth values is > good enough, and we can handle resource management on the "Occam's > razor" level > > As you already know (but others may not have thought about), weighting > possible link parses via their probabilities based on a background > corpus, is itself a form of "resource usage based Occam's razor > weighting". Because the links and link-combinations with higher > probability based on the corpus, are the ones that the OpenCog system > doing the parsing has more reason to retain in the Atomspace --- thus > for higher-weighted links or link-combinations, the "marginal memory > usage" required to keep those links/link-combinations in memory is > less. So we can view the probability weighting of a potential parse > as proportional to the memory-utilization-cost of that parse, in the > context of a system with a long-term memory full of other parses from > some corpus (or some body of embodied linguistic experience, > whatever...)..... > > Currently it seems to me that the probabilistic weighting of parses > (corresponding to possible situations) is already handling > resource-management implicitly and we don't need linear logic to do > that here... > > Of course these things are pretty subtle when you really think about > them, and I may be missing something... > > ben > > > On Wed, Aug 31, 2016 at 1:10 AM, Ben Goertzel <[email protected]> wrote: > > Linas, > > > > Actually, even after more thought, I still don't (yet) see why linear > > logic is needed here... > > > > In PLN, each statement is associated with at least two numbers > > > > (strength, count) > > > > Let's consider for now the case where the strength is just a > probability... > > > > Then in the guilt/innocence case, if you have no evidence about the > > guilt or innocence, you have count =0 .... So you don't have to > > represent ignorance as p=.6 ... you can represent it as > > > > (p,n) = (*,0) > > > > The count is the number of observations made to arrive at the strength > figure... > > > > PLN count rules propagate counts from premises to conclusions, and if > > everything is done right without double-counting of evidence, then the > > amount of evidence (number of observations) supporting the conclusion > > is less than or equal to the amount of evidence supporting the > > premises... > > > > This does not handle estimation of resource utilization in inference, > > but it does handle the guilt/innocence example > > > > As for the resource utilization issue, certainly one can count the > > amount of space and time resources used in drawing a certain inference > > ... and one can weight an inference chain via the amount of resources > > it uses... and one can prioritize less expensive inferences in doing > > inference control. This will result in inferences that are "simpler" > > in the sense of resource utilization, and hence more plausible > > according to some variant of Occam's Razor... > > > > But this is layering resource-awareness on top of the logic, and using > > it in the control aspect, rather than sticking it into the logic as > > linear and affine logic do... > > > > The textbook linear logic example of > > > > "I have $5" ==> I can buy a sandwich > > "I have $5" ==> I can buy a salad > > |- (oops?) > > "I have $5" ==> I can buy a sandwich and I can buy a salad > > > > doesn't impress much much, I mean you should just say > > > > If I have $5, I can exchange $5 for a sandwich > > If I have $5, I can exchange $5 for a salad > > After I exchange $X for something else, I don't have $X anymore > > > > or whatever, and that expresses the structure of the situation more > > nicely than putting the nature of exchange into the logical deduction > > apparatus.... There is no need to complicate one's logic just to > > salvage a crappy representational choice... > > > > In linear logic: It is no longer the case that given A implies B and > > given A, one can deduce both A and B ... > > > > In PLN, if one has > > > > A <sA, nA> > > (ImplicationLink A B) <sAB, nAB> > > > > one can deduce > > > > B <sB,nB> > > > > but there is some math to do to deduce sB and nB, and one can base > > this math on various assumptions including independence assumptions, > > assumptions about the shapes of concepts, etc. > > > > In short I think if we extent probabilistic TTR to be "TTR with <p,n> > > truth values", then we can use lambda calculus with a type system > > drawn from TTR and with each statement labeled with a <p,n> truth > > value ... and then we can handle the finitude of evidence without > > needing to complicate the base logic... > > > > A coherent and sensible way to assess <p,n> truth values for > > statements with quantified variables was given by me and Matt in 2008, > > in > > > > http://www.agiri.org/IndefiniteProbabilities.pdf > > > > Don't let the third-order probabilities worry you ;) > > > > ... > > > > In essence, it seems, the linear logic folks push a bunch of > > complexity into the logic itself, whereas Matt and I pushed the > > complexity into the truth values, and the Occam bias on proofs (into > > which resource utilization should be factored) > > > > -- Ben > > . > > > > > > > > On Tue, Aug 30, 2016 at 6:52 PM, Linas Vepstas <[email protected]> > wrote: > >> Hi Ben, > >> > >> Well, it might not have to be linear, it might be affine, I have not > thought > >> it through myself. What is clear is that cartesian is clearly wrong. > >> > >> The reason I keep repeating the guilt/innocence example is that its not > just > >> the "exclusive nature of disjuncts in link-grammar", but rather, that > it is > >> a generic real-world reasoning problem. > >> > >> I think I understand one of the points of confusion, though. In digital > >> circuit verification (semiconductor chip industry), everyone agrees > that the > >> chips themselves behave according to classical boolean logic - its all > just > >> ones and zeros. However, in verification, you have to prove that a > >> particular chip design is working correctly. That proof process does > NOT > >> use classical logic to achieve its ends -- it does use linear logic! > >> Specifically, the proof process goes through sequences of Kripke frames, > >> where you verify that certain ever-larger parts of the chip are behaving > >> correctly, and you use the frames to keep track of how the various > >> combinatorial possibilities feed back into one another. Visualize it > as a > >> kind of lattice: at first, you have a combinatoric explosion, a kind of > tree > >> or vine, but then later, the branches join back together again, into a > >> smaller collection. Those that fail to join up are either incompletely > >> modelled, or indicate a design error in the chip. > >> > >> There's another way of thinking of chip verification: one might say, in > any > >> given universe/kripke frame, that a given transistor is in one of three > >> states: on, off, or "don't know", with the "don't know" state > corresponding > >> to the "we haven't simulated/verified that one yet". The collection of > >> possible universes shrinks, as you eliminate the "don't know" states > during > >> the proof process. This kind of tri-valued logic is called > >> "intuitionistic logic" and has assorted close relationships to linear > logic. > >> > >> These same ideas should generalize to PLN: although PLN is itself a > >> probabilistic logic, and I do not advocate changing that, the actual > >> chaining process, the proof process of arriving at conclusions in PLN, > >> cannot be, must not be. > >> > >> I hope the above pins down the source of confusion, when we talk about > these > >> things. The logic happening at the proof level, the ludics level, is > very > >> different from the structures representing real-world knowledge. > >> > >> --linas > >> > >> On Tue, Aug 30, 2016 at 9:28 AM, Ben Goertzel <[email protected]> wrote: > >>> > >>> Linas, > >>> > >>> Alas my window of opportunities for writing long emails on math-y > >>> stuff has passed, so I'll reply to your email more thoroughly in a > >>> couple days... > >>> > >>> However, let me just say that I am not so sure linear logic is what we > >>> really want.... I understand that we want to take resource usage into > >>> account in our reasoning generally... and that in link grammar we want > >>> to account for the particular exclusive nature of the disjuncts ... > >>> but I haven't yet convinced myself linear logic is necessarily the > >>> right way to do this... I need to take a few hours and reflect on it > >>> more and try to assuage my doubts on this (or not) > >>> > >>> -- ben > >>> > >>> > >>> On Tue, Aug 30, 2016 at 6:14 AM, Linas Vepstas <[email protected] > > > >>> wrote: > >>> > It will take me a while to digest this fully, but one error/confusion > >>> > (and > >>> > very important point) pops up immediately: link-grammar is NOT > >>> > cartesian, > >>> > and we most definitely do not want cartesian-ness in the system. > That > >>> > would > >>> > destroy everything interesting, everything that we want to have. > Here's > >>> > the > >>> > deal: > >>> > > >>> > When we parse in link-grammar, we create multiple parses. Each parse > >>> > can be > >>> > considered to "live" in its own unique world or universe (it's own > >>> > Kripke > >>> > frame) These universes are typically incompatible with each other: > they > >>> > conflict. Only one parse is right, the others are wrong (typically -- > >>> > although sometimes there are some ambiguous cases, where more than > one > >>> > parse > >>> > may be right, or where one parse might be 'more right' than another). > >>> > > >>> > These multiple incompatible universes are symptomatic of a "linear > type > >>> > system". Now, linear type theory finds applications in several > places: > >>> > it > >>> > can describe parallel computation (each universe is a parallel > thread) > >>> > and > >>> > also mutex locks and synchronization, and also vending machines: for > one > >>> > dollar you get a menu selection of items to pick from -- the > ChoiceLink > >>> > that > >>> > drove Eddie nuts. > >>> > > >>> > The linear type system is the type system of Linear logic, which is > the > >>> > internal language of the closed monoidal categories, of which the > closed > >>> > cartesian categories are a special case. > >>> > > >>> > Let me return to multiple universes -- we also want this in PLN > >>> > reasoning. A > >>> > man is discovered standing over a dead body, a bloody sword in his > hand > >>> > -- > >>> > did he do the deed, or is he simply the first witness to stumble onto > >>> > the > >>> > scene? What is the evidence pro and con? > >>> > This scenario describes two parallel universes: one in which he is > >>> > guilty, > >>> > and one in which he is not. It is the job of the prosecutor, defense, > >>> > judge > >>> > and jury to figure out which universe he belongs to. The mechanism > is a > >>> > presentation of evidence and reasoning and deduction and inference. > >>> > > >>> > Please be hyper-aware of this, and don't get confused: just because > we > >>> > do > >>> > not know his guilt does not mean he is "half-guilty", -- just like an > >>> > unflipped coin is not a some blurry, vague superimposition of heads > and > >>> > tails. > >>> > > >>> > Instead, as the evidence rolls in, we want to find that the > probability > >>> > of > >>> > one universe is increasing, while the probability of the other one is > >>> > decreasing. Its just one guy -- he cannot be both guilty and > innocent > >>> > -- > >>> > one universe must eventually be the right one,m and it can be the > only > >>> > one. > >>> > (this is perhaps more clear in 3-way choices, or 4-way choices...) > >>> > > >>> > Anyway, the logic of these parallel universes is linear logic, and > the > >>> > type > >>> > theory is linear type theory, and the category is closed monoidal. > >>> > > >>> > (Actually, I suspect that we might want to use affine logic, which is > >>> > per > >>> > wikipedia "a substructural logic whose proof theory rejects the > >>> > structural > >>> > rule of contraction. It can also be characterized as linear logic > with > >>> > weakening.") > >>> > > >>> > Anyway, another key point: lambda calculus is the internal language > of > >>> > *cartesian* closed categories. It is NOT compatible with linear > logic > >>> > or > >>> > linear types. This is why I said in a different email, that "this > way > >>> > lies > >>> > madness". Pursuit of lambda calc will leave us up a creek without a > >>> > paddle, > >>> > it will prevent us from being able to apply PLN to guilty/not-guilty > >>> > court > >>> > cases. > >>> > > >>> > ---- > >>> > BTW, vector spaces are NOT cartesian closed! They are the prime #1 > most > >>> > common example of where one can have tensor-hom adjunction, i.e. can > do > >>> > currying, and NOT be cartesian! Vector spaces *are* closed-monoidal. > >>> > > >>> > The fact that some people are able to map linguistics onto vector > spaces > >>> > (although with assorted difficulties/pathologies) re-affirms that > >>> > closed-monoidal is the way to go. The reason that linguistics maps > >>> > poorly > >>> > onto vector spaces is due to their symmetry -- the linguistics is NOT > >>> > symmetric, the vector spaces are. So what we are actually doing > (or > >>> > need > >>> > to do) is develop the infrastructure for *cough cough* a > non-symmetric > >>> > vector space.. which is kind-of-ish what the point of the categorial > >>> > grammars is. > >>> > > >>> > Enough for now. > >>> > > >>> > --linas > >>> > > >>> > > >>> > On Mon, Aug 29, 2016 at 4:41 PM, Ben Goertzel <[email protected]> > wrote: > >>> >> > >>> >> Linas, Nil, etc. -- > >>> >> > >>> >> This variation of type theory > >>> >> > >>> >> http://www.dcs.kcl.ac.uk/staff/lappin/papers/cdll_lilt15.pdf > >>> >> > >>> >> seems like it may be right for PLN and OpenCog ... basically, > >>> >> dependent type theory with records (persistent memory) and > >>> >> probabilities ... > >>> >> > >>> >> If we view PLN as having this sort of semantics, then RelEx+R2L is > >>> >> viewed as enacting a morphism from: > >>> >> > >>> >> -- link grammar, which is apparently equivalent to pregroup grammar, > >>> >> which is a nonsymmetric cartesian closed category > >>> >> > >>> >> to > >>> >> > >>> >> -- lambda calculus endowed with the probabilistic TTR type system, > >>> >> which is a locally cartesian closed category > >>> >> > >>> >> > >>> >> > >>> >> https://ncatlab.org/nlab/show/relation+between+type+theory+ > and+category+theory#DependentTypeTheory > >>> >> > >>> >> For the value of dependent types in natural language semantics, see > >>> >> e.g. > >>> >> > >>> >> > >>> >> > >>> >> http://www.slideshare.net/kaleidotheater/hakodate2015- > julyslide?qid=85e8a7fc-f073-4ded-a2c8-9622e89fd07d&v=&b=&from_search=1 > >>> >> > >>> >> (the examples regarding anaphora in the above are quite clear) > >>> >> > >>> >> > >>> >> > >>> >> https://ncatlab.org/nlab/show/dependent+type+theoretic+ > methods+in+natural+language+semantics > >>> >> > >>> >> This paper > >>> >> > >>> >> > >>> >> > >>> >> http://www.slideshare.net/DimitriosKartsaklis1/ > tensorbased-models-of-natural-language-semantics?qid= > fd4cc5b3-a548-46a7-b929-da8246e6c530&v=&b=&from_search=2 > >>> >> > >>> >> on the other hand, seems mathematically sound but conceptually wrong > >>> >> in its linguistic interpretation. > >>> >> > >>> >> It constructs a nice morphism from pregroup grammars (closed > cartesian > >>> >> categories) to categories defined over vector spaces -- where the > >>> >> vector spaces are taken to represent co-occurence vectors and such, > >>> >> indicating word semantics.... The morphism is nice... however, the > >>> >> idea that semantics consists of numerical vectors is silly ... > >>> >> semantics is much richer than that > >>> >> > >>> >> If we view grammar as link-grammar/pregroup-grammar/asymmetric-CCC > ... > >>> >> we should view semantics as {probabilistic TTR / locally compact > >>> >> closed CCC *plus* numerical-vectors/linear-algebra} > >>> >> > >>> >> I.e. semantics has a distributional aspect AND ALSO a more > explicitly > >>> >> logical aspect > >>> >> > >>> >> Trying to push all of semantics into distributional word vectors, > >>> >> leads them into insane complexities like modeling determiners using > >>> >> Frobenius algebras... which is IMO just not sensiblen ... it's > trying > >>> >> to achieve a certain sort of mathematical simplicity that does not > >>> >> reflect the kind of simplicity seen in natural systems like natural > >>> >> language... > >>> >> > >>> >> Instead I would say RelEx+R2L+ECAN (on language) + > >>> >> word-frequency-analysis can be viewed as enacting a morphism from: > >>> >> > >>> >> -- link grammar, which is apparently equivalent to pregroup grammar, > >>> >> which is a nonsymmetric cartesian closed category > >>> >> > >>> >> to the product of > >>> >> > >>> >> -- lambda calculus endowed with the probabilistic TTR type system, > >>> >> which is a locally cartesian closed category > >>> >> > >>> >> -- the algebra of finite-dimensional vector spaces > >>> >> > >>> >> This approach accepts fundamental heterogeneity in semantic > >>> >> representation... > >>> >> > >>> >> -- Ben > >>> >> > >>> >> -- > >>> >> Ben Goertzel, PhD > >>> >> http://goertzel.org > >>> >> > >>> >> Super-benevolent super-intelligence is the thought the Global Brain > is > >>> >> currently struggling to form... > >>> > > >>> > > >>> > -- > >>> > You received this message because you are subscribed to the Google > >>> > Groups > >>> > "link-grammar" group. > >>> > To unsubscribe from this group and stop receiving emails from it, > send > >>> > an > >>> > email to [email protected]. > >>> > To post to this group, send email to [email protected]. > >>> > Visit this group at https://groups.google.com/group/link-grammar. > >>> > For more options, visit https://groups.google.com/d/optout. > >>> > >>> > >>> > >>> -- > >>> Ben Goertzel, PhD > >>> http://goertzel.org > >>> > >>> Super-benevolent super-intelligence is the thought the Global Brain is > >>> currently struggling to form... > >>> > >>> -- > >>> 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 [email protected]. > >>> To post to this group, send email to [email protected]. > >>> 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/CACYTDBeRwpZiNS% > 3DShs2YfrRbKkC426v3z51oz6-Fc8u7SoJ8Mw%40mail.gmail.com. > >>> For more options, visit https://groups.google.com/d/optout. > >> > >> > >> -- > >> You received this message because you are subscribed to the Google > Groups > >> "link-grammar" group. > >> To unsubscribe from this group and stop receiving emails from it, send > an > >> email to [email protected]. > >> To post to this group, send email to [email protected]. > >> Visit this group at https://groups.google.com/group/link-grammar. > >> For more options, visit https://groups.google.com/d/optout. > > > > > > > > -- > > Ben Goertzel, PhD > > http://goertzel.org > > > > Super-benevolent super-intelligence is the thought the Global Brain is > > currently struggling to form... > > > > -- > Ben Goertzel, PhD > http://goertzel.org > > Super-benevolent super-intelligence is the thought the Global Brain is > currently struggling to form... > > -- > You received this message because you are subscribed to the Google Groups > "link-grammar" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at https://groups.google.com/group/link-grammar. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "opencog" group. 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