From [WIkipedia](http://en.wikipedia.org/wiki/Formal_system)

> 
> 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.
> 
> 
> 

According to the same link, a formal system consists of a finite alphabet, a formal grammar, a set of axioms and a set of inference rules.

* I wonder if there are formal systems that are not logical systems?
* Does the semantics in a logical system always assign **truth values** to sentences of its formal language?

Thanks.