Is an "Alien" Language Possible?

This review of Matti Eklund's book, Alien Structure: Language and Reality, made me wonder if an alien language is even possible. Wouldn't any representational system need to use logic? When the reviewer asks, "if we wish to know whether a given language is alien, we will need some way to connect its sentences with propositions" then doesn't that mean alphabet, grammar, axioms and rules of inference that are computable (whether or not sensical)?