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Does Robust logic (Leslie Valiant), Default logic (Raymond Reiter) and Circumscription logic (John McCarthy) have any relation?

I was Mathematician and Computer Science (dual degree undergraduate) and now I'm a student of theoretical neuroscience (Ph.D.), I have a strong background in Model Theory (Logic) and Computation Theory (compatibility) because of my advisers in undergraduate, now I want to work on theories of learnability just a bit!

I am really interested in Leslie G. Valiant's works, but I can't understand his theory relation with other more famous logic in computer science and learnability.

I'll be happy if you can explain their place today, and give me some useful references.

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