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

A meaning algebra over a set of meanings $M$ is a triple $M{A}_M=⟨M,B_M,R_M⟩$, where—

1. $B_M$ is a finite set of basic meanings,
2. $R_M$ is a finite set of elementary meaning operations,
3. $M$ closes $B_M$ under $R_M$, and
4. for all $\delta ,{\delta }^{\prime }\in R_M$ and $x_1,...x_n,y_1,...,y_m$, $$\delta (x_1,...,x_n)\notin B_M$$ and, if $$\delta (x_1,...,x_n)={\delta }^{\prime }(y_1,...,y_m)$$ then $\delta ={\delta }^{\prime }$, $m=n$, and $x_i=y_i$ for $1⩽i⩽n$.