I'm looking for any extensive work on a framework for "arguments", that works something along these lines:
When two parties are debating, they are making assertions on a particular domain, D.
Those assertions are ultimately based on some axioms, A1...An of D.
An argument set, ARG is the finite set of all axioms A1...An of a domain D, and the domain D.
An effective debate is only possible if the argument set ARG1 of party P1 and the argument set ARG2 of party P2 can be shown to be equivalent.
In other words, an effective debate can be had between two parties if (and only if) they both agree on the axioms A1...An of the domain D, and the can formally define D.
- In the absence of any such agreement, no debate can be effectively had, because there is no way of proving or disproving assertions based on different sets of axioms of different domains that are not equivalent.
I noticed the possibility of such a thing existing after reading two debates. Both made good points, but disagreed not because the authors were not making reasonable arguments, but because they were simply talking about different things. And I've seen this several times in real-world arguments and debates where, confusion over how fundamental ideas are defined extends what turns out to be a needless debate.