Logic is defined as....

1. the science that investigates the principles governing correct or reliable inference.

2.a particular method of reasoning or argumentation:We were unable to follow his logic.

3.the system or principles of reasoning applicable to any branch of knowledge or study.

4.reason or sound judgment, as in utterances or actions:There wasn't much logic in her move.

5.convincing forcefulness; inexorable truth or persuasiveness:

logic is not just about mathematics....2+2=4 etc. That is only one specific type of logic.

Check out

https://en.wikipedia.org/wiki/Logic

Logic is related to culture, background and whatever seems reasonable at that time, in that social culture, with that knowledge and in that situation. For example....in a culture which is largely religious...it would be very logical to suppose that a God created the world. Logically there is no other explanation at all. To argue that the universe got generated by chance...would be very illogical and unreasonable.

In an atheist culture it would be logical to assume that some natural law generated the universe.