One can be rational "based on or in accordance with reason or
   logic." and also have justification ""the action of showing
   something to be right or reasonable." for murder. Sane
   "sensible, practical, advisable, responsible, realistic,
   prudent, wise, reasonable, rational, levelheaded,
   commonsensical, judicious, politic" shares the word rational.
   However, it's meaning is akin to a "reasonable person" and _not_
   necessarily Logic. One can use Logic and Reason to Justify
   Murder. They will consider themselves Sane, because Logic is
   Rational. But in that case, they will not fit the definition of
   a "Reasonable Man", which defines Rational differently than
   Logic. Pure Logic does not imply Sanity. Nor does it imply
   Insanity. it is unrelated. Care must be taken in defining the
   term Rational properly. It means something quite different in
   different contexts. Many a logical murderer has become confused
   at being referred to as Insane when they were being perfectly
   logical. They, in fact, were insane: "in a state of mind that
   prevents normal perception, behavior, or social interaction" -
   because they lacked what is considered "normal perception,
   behavior", etc. Social norms apply. A rational insane person can
   exist, should the rational person be rational by virtue of Logic
   rather than by what is considered "A reasonable man". However,
   all that being said: "What is a reasonable person?" really?
   That's where things get even trickier. Personally, my opinion is
   that the concept of the reasonable person should be scrapped
   entirely and replaced with "social norms". it's far more honest
   that way. I don't believe a Reasonable Man exists; and attempts
   to gauge "true intent" are quite difficult. Cognitive Science
   will slowly chip away at "free will" until there is
   justification provided (however 'insane' as it may be) that free
   will simply does not exist. Once free will does not exist, then
   no one is culpable for ANY crime. It's a slippery slope,
   externalism combined with brain scans. Remove the impetus from
   the man, and the man has no responsibility. But it's the
   direction things are going. Oh well. Eventually Science will
   likely take over the courts and i don't necessarily see that as
   a good thing. Science is not ready to be in charge of society
   just yet.