is there a kind of logic does not include if-then statements.

Two valued logic?

 

No I don't think there is a Logic that doesn't use if-then. Because if-then basically operates on whether a statement is true or false.

 

There is something called fuzzy logic which is how the functions of the brain can be modelled on, though it can be argued that fuzzy logic is still based on "yes" or "no" however it allows probability variables.