Here are few examples of words written in the alien language from "Arrival" (film):
Image source: Pinterest.
Does this alien writing have some logic in order to construct some custom meaningful sentences?
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The short answer: no, the language from Arrival is not a full conlang.
The logographs were designed by artists and designers, and, while some components of the logograms were assigned meaning, they did not define enough of its rules for it to be possible to make new symbols with definite meanings.
They did hire linguist Jessica Coon to consult on the film, and she annotated printouts of the logograms so the set designers would know what to put in the background and on the whiteboards (If I remember correctly, they consulted physicists for similar work as well). They also had Stephen and Christopher Wolfram provide some analysis and design the computer program used to analyze and generate the logograms in the film.
However, in the end, the movie was not for linguists or conlangers, so they did not design it as a fully fledged conlang—given that it's supposed to be a mystery they don't quite solve in the film, I don't think that's necessarily a bad thing.
These articles might interest you if you want more information.