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*theory*?

And how much useful is it?

I believe that most of us have an intuitive sense of logic, which has to be very useful throughout our lives and just about for every situation we can think of. Given that, I came to wonder what more does formal logic specifically brings to the table?

Obviously, having a

*formal language*to express the more complicated logical relations is very useful, even necessary nowadays with the development of technology and science, but beyond instances of using the

*formalism*of formal logic, could anybody give practical examples of using formal logic

*theory*to solve a problem in the real world? Something

*useful*!

And I would exclude from that maths research, not because I think it's hopelessly useless, but because I need to understand how logic theory is useful and I need to understand that here and now. So, using logic theory to help with applied maths would be OK, too. That is, if logic theory is used to sort out a maths problem meant to model some real-world situation, in which case logic theory would be useful to help with useful maths, and that would be obviously useful.

I'm really only interested in First Order Logic, but Second Order examples should also be of interest.

Thanks,

EB