Definition. Compositionality, computability, and complexity › General compositionality (§ 2.3) [pagin2021-general-compositionality]

A semantic system $S$ is general compositional iff for every $n$-ary operation $\sigma \in {\mathrm{\Sigma }}_L$ and every member ${\mu }_i\in S^{\prime }$ there is a meaning operation $M^n\to M$ such that for any grammatical terms $t_1,...,t_n\in Dom\sigma$ $${\mu }_i(\sigma (t_1,...,t_n))=r_{\sigma ,i}({\mu }_{j_1}(t_1),...,{\mu }_{j_n}(t_n)),$$ where for $1⩽k⩽n$ $${\mu }_{j_k}={\mathrm{\Phi }}_S({\mu }_i,\sigma ,k).$$