Feature request: add the "underpin"-relation as a positive analogue of the undercut relation

[tobias-martin]

Dear @christianvoigt,

This is an old idea I've discussed with @ggbetz in September 2021 after a workshop of yours: to add a positive analogue of the undercut relation. Hence, like undercut, it is a relation defined just between arguments. He suggested to write this feature request, yet, due to illness, I was unable to this until now.

I thought of "underpin" as a nice name for this relation. In German I call it "unterstützen" in contrast to "untergraben". Back in 2021, @ggbetz suggested another nice name for this relation, "underscore". Yet, this term is already in use in its usual meaning of typing "_". Furthermore "underpin" is a closer translation of "unterstützen". Choose any term you like!

Additionally, I have a request concerning the arrowtypes. As of now, if I am correct, all relations have the same arrowtype. The addition of underpin would make it necessary to use a fourth color for distinguishing it from the other three relations. Yet, I would like to use two different arrowtypes: one for the pair support and attack (arrowhead="normal"), and one for the pair underpin and undercut (e.g. arrowhead="tee"). Being positive relations, support and underpin would have the same color (color="green"). Another color would be shaired by the negative relations attack and undercut (color="red"). (For some eludications on underpin and undercut being relations best represented by arrows with the same arrowtype, see below.)

Thank you very much for your beautiful work on argdown! I love it. All the best
Tobias

p.s.:

• In my writing and teaching, I use the underpin relation as a simplistic reconstruction of Toulmin's warrant. An argument A underpinning an argument B most easily can be thought of as A's conclusion being the conditional from the conjunction B's premises to B's conclusion (thus supporting the inference from B's premises to its conclusion). On the contrary, an argument A undercutting an argument B can be thought of as A's conclusion negating the conditional from the conjunction of B's premises to B's conclusion (thus attacking the inference from B's premises to its conclusion).
• Undercut and underpin have some relevance to Justifications on Relations #302.
• Your Assumptions in Argument Reconstructions #42 will potentially benefit the implementation of underpin and undercut in the following way: The introduction of assumptions is a necessary condtition for the introduction of conditionalizations (conditional proofs). Since the conclusion of an underpinning argument can most easily be reconstructed as a conditional, a conditional proof would be a natural form of underpinning arguments.