Definition:Subsignature

Definition
Let $\mathcal L, \mathcal L'$ be signatures for the language of predicate logic.

Then $\mathcal L$ is said to be a subsignature of $\mathcal L'$''', denoted $\mathcal L \subseteq \mathcal L'$,, for each $n \in \N$:


 * $\mathcal F_n \left({\mathcal L}\right) \subseteq \mathcal F_n \left({\mathcal L'}\right)$
 * $\mathcal P_n \left({\mathcal L}\right) \subseteq \mathcal P_n \left({\mathcal L'}\right)$

where $\mathcal F_n$ denotes the collection of $n$-ary function symbols, and $\mathcal P_n$ denotes the collection of $n$-ary predicate symbols.

Also see

 * Definition:Signature for Predicate Logic


 * Definition:Expansion of Structure
 * Definition:Reduct of Structure