The problem with logic is it operates in a confined space and relies on stringent definitions and rules. To know whether or not A is true or false we need to know the value of ~A and vice versa. In the case of the absurd, we cannot know the absolute value of either, so we project values and operate based on the values we accept as true regardless if they are true unilaterally. The problem with logic and international law – or any law for this matter – is that people’s definition of true and false, for an identical statement, differ fundamentally in certain cases. It is in these cases that conflicts develop out of the convention of definitions and their associated truths. In cases where both parties can agree on the associations of truth for given premises, conflicts are unlikely to develop and a valid conclusion can be arrived at. How can we use logic appropriately while accounting for the inherent inconsistencies between cultures and organizations of people? If we can structure an argument around the basic, universally accepted principles of morality and human nature, then we can begin to engage in conversation. But what happens when conflicts arise between “universally” accepted truths in cases dealing with religious, spiritual, and unquantifiable realities? Can we perform logic on abstract ideas given their innate incompleteness? If we approach questions of logic with as much objectivity as we are afforded in life and clearly state assumptions where we must, then logic should provide a baseline for action. Given a sound baseline, we must then operate on behalf of our current circumstance and understanding to approach a wide-ranging and inclusive conclusion.
B.W. 
I think the fact that logic is bound by stringent rules is a good thing overall, although. That’s what allows it to be such a powerful form of argument. It’s a foundation. It’s true that people can come to different conclusions (true/false, moral/immoral) for the same action. However, we should then evaluate the consistency of the two parties in applying the principles in the given statement to other, similar statements or implications. Consistency is a necessary principle of logic. If somebody proposes that a fundamental principle is true, then there are almost an infinite amount of conclusions they logically should say are true/false based on that statement. If however, they show inconsistencies in their line of thought and/or application, one of the following two things is happening.
1) They are unaware of the inconsistencies.
2) They are aware, but refuse to change their position.
If the former, then we should do what we can to make them aware (albeit we have to understand their revelation may not be immediate).
If the latter, then they are acknowledging that they don’t value truth, and we shouldn’t waste endless amounts of time trying to convince them.
I agree overall. The rules and structure of logic are what make it useful and enable us to draw sound conclusions from valid arguments. In a formal application of logic, we can follow these rules and formulate sound conclusions. Like you said though, the problem arises when the people applying logic are basing their arguments on premises which are inconsistent. In order for a conclusion to be applicable in situ, the parties involved must agree on the validity of the statements. If they don’t, they can arrive at two different conclusions even after applying sound logical reasoning. In cases of imperialism, as an example, two parties have differing ideas of true and false based on their needs, wants, and circumstance. Therefore the carrying out of action is no longer grounded in matters of truth and logic, but are leveraged through power. When power or authority enters the equation – logic being a model for “correctness” – then the sovereignty which logic and truth affords us is no longer present; people are simply maneuvered by force to either consent (with a gun to their head) or resist.