Does a logical system have semantics?

From Wikipedia:


A logical system or, for short, logic, is a formal system together with a form of semantics, usually in the form of model-theoretic interpretation, which assigns truth values to sentences of the formal language, that is, formulae that contain no free variables. A logic is sound if all sentences that can be derived are true in the interpretation, and complete if, conversely, all true sentences can be derived.

Does a logical system have semantics?

Does the assignment of truth values to sentences of the formal language count as the semantics of a logical system? I feel it provide little interpretation of what the sentences of the formal languages mean.

Semantics of a logic describe how to compute the truth value of an expression, possibly given some interpretation. For example, one rule would say that an expression $\varphi \land \psi$ is true iff both $\varphi$ and $\psi$ are true, and another would say that $\forall x \varphi(x)$ is true if for all $x$ in the domain of discourse $D$ (which forms part of the interpretation).

Sometimes the semantics are not obvious – for example, there are different semantics for modal logic. Sometimes we are interested in non-standard semantics, such as
the semantics of bounded arithmetic described in Forcing with random variables.

StackExchange Computer Science Q#28446, answer score: 8