ifc-0268

18.2 The second direction: proto-accommodation and semantic extension

Let \(\mathbb L_{\mathrm{vis}}\) be a visual-language sketch. Its sorts may include object, attribute, relation, scene, and transformation; its arrows encode composition, binding, part–whole maps, viewpoint, and rendering constraints. A model of \(\mathbb L_{\mathrm{vis}}\) is a semantic scene. A rendering semantics assigns not one canonical image but a distribution:

\[ \mathcal F_\theta : \operatorname {Mod}(\mathbb L_{\mathrm{vis}},\mathcal C) \longrightarrow \mathsf{Prob}(\mathcal X). \]

Ordinary conditional generation moves horizontally through image–noise space while holding \(\mathbb L_{\mathrm{vis}}\) fixed. ARTISTIC adds a vertical, proto-accommodative direction that probes whether a visual primitive, relation, formation rule, binding law, or conditioning interface is missing. Infinitesimal language probes vary the current semantic realization locally. If they motivate a finite proposal, the proposed semantic extension is recorded as

\[ \mathbb L_{\mathrm{vis}}\longrightarrow \mathbb L_{\mathrm{vis}}^+. \]

An actual new word or grammatical constructor becomes accommodation only after this extension and its transported models are independently admitted.

Let \(\tau _u:\ell \to \ell _u\) be a small language-side transport and let \(\widehat\tau _u^t:\mathcal X_t^\ell \to \mathcal X_t^{\ell _u}\) denote its registered realization on image states at noise time \(t\). The mixed square then compares

\[ \Phi _{s,t}^{\ell _u}\circ \widehat\tau _u^s \qquad \text{with}\qquad \widehat\tau _u^t\circ \Phi _{s,t}^{\ell }. \]

The comparison need not be a pixelwise subtraction. It is a typed mate whose realization may be scored through object, relation, and rendering observers. Its defect asks whether changing the intended semantics before denoising agrees with transporting those semantics through an existing denoising flow.