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Lethal Autonomous Weapons promise to revolutionize warfare -- and raise amultitude of ethical and legal questions. It has thus been suggested to programvalues and principles of conduct (such as the Geneva Conventions) into themachines' control, thereby rendering them both physically and morally superiorto human combatants.  We employ mathematical logic and theoretical computer science to explorefundamental limitations to the moral behaviour of intelligent machines in aseries of "Gedankenexperiments": Refining and sharpening variants of theTrolley Problem leads us to construct an (admittedly artificial but) fullydeterministic situation where a robot is presented with two choices: onemorally clearly preferable over the other -- yet, based on the undecidabilityof the Halting problem, it provably cannot decide algorithmically which one.Our considerations have surprising implications to the question ofresponsibility and liability for an autonomous system's actions and lead tospecific technical recommendations.

Logical Limitations to Machine Ethics with Consequences to Lethal Autonomous Weapons