I have the following definition of intransitivity:
R is intransitive iff
for all xyz: xRy & yRz -> ~xRz
Now, given the following: aRb bRc cRd
Can I conclude that ~aRd?
Intuitively, I would say yes*, but I'm having problems with the formal proof.
*For example, if R would be 'is a parent of', and incest is impossible, clearly a is not a parent of d. But how to prove that?