NOT.3:11 - SoTA-Echoing
| Source and contribution | Adoption and limit |
|---|---|
| Macbeth, Seeing How It Goes: Paper-and-Pencil Reasoning in Mathematical Practice, 2011, opening discussion and treatment of Peirce’s alpha graphs, historical foundation | Adopt the distinction between recording an answer and working through signs to obtain or expose reasoning. Her different readings of a graph motivate retaining useful reading routes. Their mathematical case does not establish equal accessibility to every reader. |
| Dutilh Novaes, Formal Languages in Logic, 2012, §5.2, historical foundation | Adapt attention to the operations people perform with external inscriptions and the preparation those operations require. Treat the cited human studies at their studied scope; no general learning gain or cross-agent equivalence follows here. |
| Piedeleu and Zanasi, An Introduction to String Diagrams for Computer Scientists, mathematical syntax/semantics account | Use compositional interpretation when the notation and target operations admit it: the whole interpretation follows the specified combination of parts. This offers a formal alternative to a merely demonstrated reading. The required obtaining procedure and the reader’s access still depend on the intended use. |
Choice between approaches. If a known formal interpretation and an available evaluator already answer the question, use them; a new reading procedure adds no value. When the difficulty is obtaining the consequence from a new notation, the present method supplies that route and locates its tacit requirements. A trained reading can be useful before a full formal calculus exists; a broader preservation or automation claim can justify constructing that calculus through the mathematical and computational suppliers.