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Deep learning is based on getting a large number of samples and essentially making statistical deductions and outputting probabilities.

On the other hand we have formal programming languages like PROLOG which don't involve probability.

Is there any essential reason why an AI could be called conscious without being able to learn in a statistical manner? i.e. by only being able to make logical deduction alone. (It could start with a vast number of innate abilities).

Or is probability and statistical inference a vital part of being conscious?

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    $\begingroup$ specific answers to your question must be speculative.It will be much more better if you narrow down your question. $\endgroup$ – quintumnia Jul 23 '18 at 18:27
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Computational Learning Theory gives us an interesting framework to understand what statistical learning is doing.

The gist of it is, we can model the process of statistical learning as one of formal deduction. The learning itself does not require a random element.

This shouldn't be too surprising. Consider a classic decision tree learner like C4.5 or ID3: the algorithm works through the data deterministically, and no random decisions are made. When asked to make a prediction, the learned model returns the frequency of each possible label within the most similar subpopulation from its training data, with similarity defined according to the algorithm's rules for partitioning data.

There's no reason you can't write a decision tree learner (or even a deep learning algorithm) in Prolog, it just might not be very efficient, or very practical.

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