a logic based moral system? morality is an issue of ethics. it is a matter of philosophy. yes, there is logic too it, but even non-religious moral philosophies aren't entirely logic based. moral relativism itself is a highly self-contradicting ethical stance on many levels to the point of even being self-defeating. it does not address a point of reference nor does it give a sufficient explanation as to what morality is, where it comes from, and why it is there.
i will not argue that there are moral grounds that can justify killing another human being. and i the issue of zygotes to me is a bit gray, but i will not concede that a fetus is in fact human. it has a beating heart and is consistent with the conventional definitions for life with the exception of reproduction, which won't even develop til the child reaches puberty anyway. to kill it merely because i don't want it, doesn't seem morally sound because it could give me ethical grounds to say, because i don't like you i can kill you. i'm sure you will agree that merely wanting the death of someone that is alive does not justify killing.