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Perceptrons, a simple form of supervised machine learning, must be trained with a set of known good inputs before they can "learn" by adjusting internal weights assigned to inputs, based on the accuracy of its results.

Similarly, we know that reinforcement learning and unsupervised neural networks are able to learn without any known model of the problem; they can be designed to collect information about an environment only by interacting with it.

Can symbolic AI be used to design a system that can achieve this "naive learning," or is this a property exclusive to certain soft computing techniques?

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What's the difference between having known good inputs and interacting with the environment? In both cases, you have inputs to the learning algorithm that get a value of some sort. (Similarly, perceptrons are artificial neural nets, their failing being the linear functions in the nodes.)

There are various sorts of unsupervised learning algorithms, although since they don't have known answers they primarily work by sorting inputs into various classes. One simple one is to represent inputs with N values in N-space, and using clustering algorithms to get classifications.

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The symbolic methods of machine learning encompass both supervised and unsupervised learning.

Supervised symbolic learning covers mining logical rules and dependencies from data:

and also learning concepts from data:

For unsupervised symbolic learning the well known example is conceptual clustering.

So supervised and unsupervised learning aren't a sub-symbolic (i.e. artificial neural networks, Bayesian classifiers...) only AI topic.

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