Your definition of causality seems sufficient, but you may want to mention in your definition of non-causal if the outputs are only affected by future inputs or if past and present inputs can affect the output as well. -Ryan Scott
Your definitions of causal and non-causal systems look good to me. -Christen Juzeszyn
Your definitions look good. You may want to consider adding some examples as well. - Joseph Mazzei
Correct and to the point - Ronny Wijaya