What does irrationality mean under the notion of revealed preferences? An example with terrorism. I am currently studying for an economics of conflict exam and one of the potential questions is likely to be in the vein of "Are Terrorists Rational - Discuss".

However how would rationality be defined in this context?

A canonical example is often metal detectors, whereby it is has been shown that when metal detectors were introduced in airports, terrorists substituted skyjackings for other means hostage taking. This would imply some rational framework where terrorists have some sort of budget constraint and indifference curve.

However, under the assumption that they didn't substitute for another form of terrorist action, would this imply irrationality? On a superficial level it may, but what if they just valued skyjackings really highly? Under the notion of revealed preferences, surely by just attempting to skyjack you are showing that skyjacking is valued to you and you are therefor doing a "rational" action?

So can something ever be irrational?
I think I have worked out some sort of solution to this question.

In Handbook of Defense Economics Chapter 9: Terrorism Theory and Applications, Enders and Sandler give the example of metal detectors in airports to explain the notion of rationality under terrorism. 

They show empirically that the inclusion of metal detectors in airports not only decreased the number of skyjackings, but that terrorists substituted towards other means such as more conventional hostage taking. They also give the example of when America fortified their embassies, terrorists attacked America's allies' embassies more. These substitution effects are an example of rationality as either cost benefit analysis is being applied or there optimization with constraints is taking place.

However, my question related to "What if skyjackings didn't decrease after metal detectors were put in", would this imply terrorists aren't rational and we can't use these models to understand their behavior?

The answer to this is that we don't know and that two competing solutions exist: 

(1) Terrorists are irrational and act arbitrarily to express anger.

(2) Terrorists simply don't have full information or their preference for skyjacking is extremely high. In this case they could have done a cost benefit analysis but may have calculated incorrectly or not been privy to full information.

I lean towards the later, but it is impossible to prove either.