They're not assumptions, they're conclusions. Inference is a form of logic, too. We observe that nature has been reliable so far, and conclude in the absence of a good reason to think otherwise, that it will continue to do so. So far, so good. The brain's ability to interpret reality can be checked against reality, in fact, you could argue that one of the main services that science provides is a way to check our brains against reality, and the best that can be said for our brains and reality, is that they do a pretty good job at the scale they operate on, considering. As you say, logic is consistent by its nature, if it weren't, it wouldn't have rules that we can discover.
Science's only assumption is that reality is real.