In Civilization V, whenever you catch a spy trying to steal a technology and identify who his master is, you are presented with three options.
1. To forgive them for spying on you
Which gives a diplomatic boost with that civilization.
2. To ask them to stop spying on you
Which results in a diplomatic penalty with that civilization.
3. To declare war
Warring is often difficult due to the warmonger penalties. I know that whenever one declares war on a civ teaming with another through 'Should we declare war on...?', the warmonger penalty is halved.
Know that the Warmonger Penalty is cut in half any time you have agreed to go to War against a Civ at another's request, or asked them to do this through the Diplomacy interface (Shall we declare war upon...).
Is the warmonger penalty for declaring war upon discovering a spy, reduced by the fact that you just caught them spying?