Definition. Compositionality, computability, and complexity › Semantic algebras (§ 3) [pagin2021-semantic-algebra]

A semantic algebra over a language $L$ and domain $M$ of meanings is a triple $$S{A}_{L}M=⟨⟨G{T}_L,M⟩,⟨A{T}_L,B_M⟩,⟨{\mathrm{\Sigma }}_L,R_M⟩⟩$$ where—

1. $⟨G{T}_L,A{T}_L,{\mathrm{\Sigma }}_L⟩$ is a grammatical term algebra for $L$, and
2. $⟨M,B_M,R_M⟩$ is a meaning algebra for $M$.