On Sat, Jan 2, 2021, 2:47 PM Ben Goertzel <[email protected]> wrote: > > > "Paraconsistent Foundations for Probabilistic Reasoning, Programming > and Concept Formation > " > > https://arxiv.org/abs/2012.14474
Extensions to Boolean logic are mathematically interesting. But it isn't clear to me how "both true and false" and "neither true nor false" differ in real life, or what is to gain by having both as separate concepts. Have you done any experimental evaluation of different logics? I have, and it is quite a bit of effort to optimize both candidates to get a clear answer. In PAQ6 I use probabilistic logic with both a probability and a confidence. In PAQ8 I used a single valued probability with an implied high confidence for values near 0 or 1. It took a couple of years with people competitively optimizing both methods to establish the latter as superior. The former had already achieved top rankings in several benchmarks including the Calgary challenge before being topped by the latter. In PAQ6, the assertion "the next bit is 1 in context X" has probability r/n and confidence n, where a 1 bit was previously observed r out of n times in context X. To combine predictions in contexts X and Y you add the counts, like probability (rx + ry)/(nx + ny) and confidence nx + ny. These can also be adaptively weighted. There are practical considerations like how do deal with large counts overflowing. In PAQ8, a probability p = r/n has an implied confidence of 1/(p (1-p)). To combine predictions you average them in the logistic domain, x = ln(p/(1-p)) using adaptively weighted averaging. The result is converted back to a probability by the inverse, p = 1/(1 + e^-x). The adaptive weighting is effectively a neural network trained by gradient descent in coding cost space. PAQ8 is simpler, with nice mathematical properties. But that doesn't necessarily make it better. You can only determine that experimentally with a lot of work. > > ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/T425c68f0cea319cd-M013558b6102ddf4bd14abb92 Delivery options: https://agi.topicbox.com/groups/agi/subscription
