Definition. Compositionality, computability, and complexity › Standard compositionality (§ 2.2) [pagin2021-standard-compositionality]

Given a grammatical term algebra $GT{A}_L$ and domain $M$ of meanings, a semantic function $\mu :G{T}_L\to M$ is standard compositional iff for every $n$-ary operation $\sigma \in {\mathrm{\Sigma }}_L$ there is a meaning operation $r_{\sigma }:M^n\to M$ such that for any $t_1,...,t_n\in Dom\sigma \subseteq G{T}_L$, $$\mu (\sigma (t_1,...,t_n))=r_{\sigma }(\mu (t_1),...,\mu (t_n)).$$