I normally use the word rational, because that includes scrutinizing the evidence.
"I met a very interesting person who had very logical reasons for believing the world did not exist. He started with some flawed assumptions, but used correct logic and reasoning from there on. "
Puzzles are cute, but it wasn't a rational construction. When the conclusion contradicts reality, the logic is bad.
"Logic is a great tool, but a very fearsome master. If all I used was logic and reason, then I could find no reason not to kill all unproductive members of society."
Logic is a process to be used to examine relationships between things and discover truths. It can not be a master anymore than a voltmeter can be a master.
If you can find no justification for coming to the conclusion that you have no right to take the life of another, for any reason other than to protect your rights from imminent violation, then you are not being logical whatsoever. If you require an appeal to authority for justification. You are not being logical whatsoever.
"Some British doctors are using logic just like that to push for the killing of handicapped children."
That is socialism. It's a arbitrary philosophy, not logic. The philosphy that a few experts, or "representatives" have the rightful place and duty to dictate is also behind the bulk of American law also. Without a fundamental respect for individual life and rights, there is no logic to the philosophy.
No the logic is bad when it is bad logic - when it violates the rules of logic - period.
"People who always kill their young are good; Sally always kills her young; Sally is good." contains no flaw in logic.