Definition:Formal Semantics/Structure

Definition
Let $\mathcal L$ be a formal language.

Part of specifying a formal semantics $\mathscr M$ for $\mathcal L$ is to specify structures $\mathcal M$ for $\mathscr M$.

A structure can in principle be any object one can think of.

However, to get a useful formal semantics, the structures should support a meaningful definition of validity for the WFFs of $\mathcal L$.

It is common that structures are sets, often endowed with a number of relations or functions.

Also see

 * Definition:Validity