Epi is a common greek prefix. It means “on top of” but can have extremely varied meanings depending on the word. And in your case, both words use similarly rooted greek words based on “logos”. Logos can mean “logic” or “speech” or a billion other things.

Thats how “epilogue” can mean “the end of a text/speech/movie”(on top of/in addition to the text/movie) and “epilogenic” is not a real word but i guess can mean “using logic to decide”.

Logos is definitely one of the cooler looking words, especially when written in capital greek letters ΛΟΓΟΣ. So angular.