It is my opinion that as far as mathematics is concerned it does not make a big difference which field one is working in. In general some real problem is first, followed by an abstraction. Anything resulting from this abstraction is what I would call the workflow of mathematics. Take for instance argumentation theory.

Standard argumentation theory is a philosophical science. It deals with anything close to an argument: disputes, the balance of pros and cons, truth in court and so on. In 1995 Phan Minh Dung presented an as of now widely accepted abstraction of argumentation principles. Although wikipedia lists Dung's work under artificial intelligence or non-monotonic logic, for me it is just mathematics, or maybe logic respectively mathematical foundations.

In abstract argumentation we deal with arguments (which are the basic elements) and attacks (which consist of well-ordered pairs of arguments). This is the basic abstraction and this is as much as this posting is explaining abstract argumentation. Of course there are inferences with classical argumentation theory and, since abstraction does not care if it is applied to the original field, also with quiet different theories. But I am actually happy to stay with theoretical problems resulting from this abstraction.

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