It seems to me that the concept of an argument is closely related to the idea of bounded rationality. Given any way in which rationality can be bounded, there is probably a form of argument which (if applied properly) can assist a particularly bounded agent to achieve feats of rationality that would otherwise be beyond its bounds.
By this reasoning, there are as many forms of argument as there are forms of bounded rationality.
You may find it useful to look into “proof assistants” like Agda. In a sense, they allow you to feed in an ‘argument’ in the form of proof sketches, proof strategies, and hints, and then to automatically generate a checkable proof.
It seems to me that the concept of an argument is closely related to the idea of bounded rationality. Given any way in which rationality can be bounded, there is probably a form of argument which (if applied properly) can assist a particularly bounded agent to achieve feats of rationality that would otherwise be beyond its bounds.
By this reasoning, there are as many forms of argument as there are forms of bounded rationality.
You may find it useful to look into “proof assistants” like Agda. In a sense, they allow you to feed in an ‘argument’ in the form of proof sketches, proof strategies, and hints, and then to automatically generate a checkable proof.