In his analysis of the Kenyan Shopping Mall attack, Tom Rogan provides an excellent succinct explanation of the justification for Islamic Jihad. It's a "blend of theocratic absolutism and perverse consequentialism".
Of course, this raises a key question: How do the jihadists excuse their atrocities?
In the blend of theocratic absolutism and perverse consequentialism. From the jihadist perspective, their violence is justified in the service of God’s intrinsic will.
Grappling with this notion of ordained will is crucial. It affords us insight into the existential rigidity with which these terrorists regard the world. In short, Salafi Jihadists claim that the price of peace is our non-interference — they hint that our acquiescence will buy us our safety. They’re lying. Theirs is an ideology with a supra-national (and, as they see it, divine) pursuit — a global caliphate of absolute power. Take al-Shabab. As Beifuss and Bellini note in their study of terrorist iconography, Branding Terror, al-Shabab’s logo, a rifle-sheltered Koran sitting upon a green globe, is unmistakably clear in its prevailing message: This group will never find satisfaction in local politics.
Emphasis on "they're lying" is mine. Because if you are willing to murder in the name of God, you are willing to tell lies for sure. As well as to ignore those cute, little "no guns allowed" stickers.