lin-0228

19.1 The Toulmin learning sketch

Let

\[ \mathbb S_{\mathrm{Arg}} = (S_{\mathrm{Arg}}, \mathcal D_{\mathrm{Arg}}, \mathcal L_{\mathrm{Arg}}, \mathcal K_{\mathrm{Arg}}) \]

be the argument learning sketch. Its objects include claims \(C\), grounds \(G\), warrants \(W\), backing \(B\), qualifiers \(Q\), rebuttals \(R\), source-bearing proposition clusters, local tickets, compatible families, and admitted global arguments.

Its arrows perform role extraction, source pullback, restriction, warrant licensing, backing support, qualifier scoping, rebuttal discharge, graph incidence, local-to-global realization, and projection to a downstream decision.

The declaration contains four particularly important path obligations.

Warrant transport.

Restricting a warranted argument must agree with restricting its grounds, warrant, and claim before reconstructing the local bridge:

\[ \rho _C\! \left(W(G)\right) \cong \rho _W(W)\! \left(\rho _G(G)\right). \]

Source naturality.

A transported claim must retain the source restriction that licensed the grounds. Source erasure is a path failure even if the surface claim is unchanged.

Qualifier and rebuttal preservation.

Transport may tighten a qualifier but cannot silently strengthen the claim. A rebuttal must remain explicit, be discharged by a declared evidence-bearing rule, or block promotion.

Descent and effectivity.

Compatible tickets form a cone over their overlap diagram. A distinct realization map determines whether that compatible family is an admissible global argument.