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Why there is so comparatively little work in machine learning using mathematical logic? Most of the research uses methods in (Bayesian) statistics, linear algebra, numerical analysis and so on. However, almost no use of, for instance, relevant logics is made.

My background is in philosophy, not computer science. But given that logic is in the business of analyzing the notion of inference I was rather surprised to learn that machine learning and other branches of AI research do not rely on mathematical logic as much as I thought they would. What about non-monotonic logics in drawing inferences or modal logic? It seems to me that it is mostly philosophers and some, dare I say, older people in cs departments that work in logic?

Are the reasons practical (easier implementation of methods from other areas), sociological (machine learning/AI was started by non-logicians), or theoretical (the bulk of machine learning is mostly about categorising and analyzing data, because that is the hard part, and less drawing inferences).

As a closer: Is there any chance that mathematical logic will have greater influence on machine learning in the future?

All the best!

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  • $\begingroup$ Thanks for the answer. I came across that thread before and was irritated by the wide range of answers. $\endgroup$ – Maximilian Stöckel Jan 14 '19 at 10:39
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I think the reason why formal logic is not widely used is its strictness. Also, it has quite restricted area of application and requires the domain to be formalized first. In contrast to that, ML methods can be fuzzy, robust to noise and work well for real-life data.

Here is an interesting discussion on the topic: https://www.quora.com/Whats-the-relationship-between-mathematical-Logic-and-Machine-Learning

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I think your answer (or rather your perspective) is driven greatly depending on which part of "machine learning" you're looking at. It's a broad field and the approaches within each practice are different. An NLP specialist is going to have a different approach than an image processing specialist who will also be different than a signal processing expert.

Also, are you reading whitepapers or looking at entire case studies of production implementations. If you do nothing but read whitepapers, then yes, it's easy to say that machine learning is myopic with "just math". But that's missing the forest for the trees. When you take a step back and look at large scale implementations, where you are combining multiple algorithms into a finished solution then it's clear that various forms of logic are used along the way.

As an example, let's consider autonomous cars. There is no one algorithm that runs the car - autonomous driving is a combination of various algorithms and machine learning approaches. You can read the individual whitepapers and not see any logic there, it's strictly math. But when you look at how the components come together to make a car go forward, the use of logic becomes clear.

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