Figure 2

Partial rule composition. (a) Commutative diagram of the composition (L, K, R) = (L₂, K₂, R₂) ∘ (L₁, K₁, R₁), with arrows denoting subgraph isomorphisms. Not shown is that L₂ is the disjoint union of $\overline{L_2}$ and $L_2^{\prime }$, i.e., $L_2=\{\overline{L_2},L_2^{\prime }\}$). Additionally, $L=\{L_1,L_2^{\prime }\}$, $C_1=\{K_1,L_2^{\prime }\}$ and $E=\{R_1,L_2^{\prime }\}$. (b) Illustration of the subgraph relations of a partial composition: $L_2^2$ is a subgraph of R₁, R₂ is a subgraph of the resulting right side R.