And so here is the blog post -- its a lightly reformatted version of this email, with lots of links to wikipedia and a few papers.
http://blog.opencog.org/2016/08/31/many-worlds-reasoning-about-reasoning/ I really really hope that this clarifies something that is often seen as mysterious. --linas On Wed, Aug 31, 2016 at 4:16 PM, Linas Vepstas <[email protected]> wrote: > 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+a >> nd+category+theory#DependentTypeTheory >> >>> >> >> >>> >> For the value of dependent types in natural language semantics, see >> >>> >> e.g. >> >>> >> >> >>> >> >> >>> >> >> >>> >> http://www.slideshare.net/kaleidotheater/hakodate2015-julysl >> ide?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+metho >> ds+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%3D >> Shs2YfrRbKkC426v3z51oz6-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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