Pei, Thanks for your thoughtful comments! Here are some responses...
--------- *. "S = space of formal synapses, each one of which is identified with a pair (x,y), with x Î N and y ÎNÈS." Why not "x ÎNÈS"? --------- No strong reason -- but, I couldn't see a need for that degree of generality in a Hebbian Logic context... of course, there's no reason not to allow it in a formal model. ------- *. "outgoing: N à S*" and "incoming: N -> S*" Don't you want them to cover "higher-order" synapses? ------- Yeah, you're right. However, I may remove higher-order synapses from the paper entirely, preferring to deal with higher-order relations via links to "multi-neuron" paths as discussed later on. --------- *. "standard neural net update and learning functions" One thing I don't like in NN is globle updating, that is, all activations and weights are updated in every step. Even if it is biologically plausible (which I'm not sure), in an AI system it won't scale up. I know to drop this will completely change the dynamics of NN. ---------- Actually, in attractor neural nets it's well-known that using random asynchronous updating instead of deterministic synchronous updating does NOT change the dynamics of a neural network significantly. The attractors are the same and the path of approach to an attractor is about the same. The order of updating turns out not to be a big deal in ANN's. It may be a bigger deal in backprop neural nets and the like, but those sorts of "neural nets" are a lot further from anything I'm interested in... ----------- *. "probability P(A,t), defined as the probability that, at time t, a randomly chosen neuron xÎA is firing" and "the conditional probability P(A|B; t) = P(A ÇB,t)/ P(B,t)" This is the key assumption made in your approach: to take the frequency of firing as the degree of truth. I need to explore further about its implications, though currently I feel uncomfortable. In my own network interpretation of NARS (for a brief description, see http://www.cogsci.indiana.edu/farg/peiwang/papers.html#thesis Section 7.5), I take activation/firing as a control parameter, indicate the recourse spends on the node, which is independent to the truth value --- "I'm thinking about T" and "T is true" are fundamentally different. Of course, the logic/control distinction is not in NN, where both are more or less reflected in activation value. When you map their notions into logic, such a distinction become tricky. ----------- Yeah, to make Hebbian Logic work, you need to assume that frequency of firing roughly corresponds to degree of truth -- at least, for those neural clusters that directly represent symbolic information. So, for instance, the "cat" cluster fires a lot when a real or imaginary cat is present to the mind. If the mind wants to allocate attention to the "cat" cluster, but there is no real cat present, it must then either -- find a way to stimulate other things logically related to "cat" -- create abstract quasi-perceptual stimuli that constitute a "mock cat" and "fool" the "cat" cluster into firing I think this is how the brain and human mind work. I agree it's not optimal, and that in an AI system it's nicer to make separate parameters for activation and truth value, as is done in both NARS and Novamente. ------------- *. Basic inference rules I don't see what is gained by a network implementation (compared to direct probabilistic calculation). ------------- Actually, I think there is no big advantage. This issue is discussed in the very last section of the paper. My view is that the brain uses a horribly inefficient mechanism to achieve probabilistic inference, and AI systems can achieve the same thing more efficiently. I prefer the Novamente implementation of PTL to a Hebbian Logic implementation. However, I think it's interesting to observe, theoretically, that a Hebbian Logic representation is possible. ------------- *. Hebbian Learning The original Hebbian learning rule woks on symmetric links (similarity, not inheritance), because weight of a link is decrease when one end is activated and the other isn't, and which is which doesn't matter. What you does in "Hebbian learning variant A" is necessary, but it is not "the original Hebbian learning rule". ---------------- Oops, you are right. My variant A is fairly standard in the literature these days, but it's not the original one. I will correct that, thanks. ---------------- *. Section 6 I'm not sure I understand the big picture here. Which of the following is correct? (1) PTL is fully justified according to probability theory, and the NN mechanism is used to implement the truth value functions. (2) PTL is fully justified according to probability theory, and the truth value functions are directly calculated, but the NN mechanism is used to implement inference control, that is, the selection of rules and premises in each step. (3) The logic is partially justified/calculated according to probability theory, and partially according to NN (such as the Hebbian learning rule). ------------- Option 1 is correct. --------------- *. In general, I agree that it is possible to unify Hebbian network with multi-valued term logic (with an experience-grounded semantics). NARS is exactly such a logic, where a statement is a link from one term to another, and its truth value is the accumulated confirmation/disconfirmation record about the relation. In NARS, Hebbian learning rule correspond to the comparison (with induction, abduction, and deduction as variants) plus revision. Activation spreading corresponds to (time) resource allocation. ----------------- Hmmm.... Pei, I don't see how to get NARS' truth value functions out of an underlying neural network model. I'd love to see the details.... If truth value is not related to frequency nor to synaptic conductance, then how is it reflected in the NN? -- Ben ------- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/[EMAIL PROTECTED]
