# Inconsistencies in a set of conditions

I am looking for algorithms to find inconsistencies in a set of IF-THEN-ELSE conditions. I am aware of lambda calculus as a model to represent these. Are there any other models?

Example
Then rules if (a & b) then X and if (a & b) then Y are contradictory because of the condition on a and therefore inconsistent. The rules if (a) then X and if (a | b) then Y are overlapping. I am looking for a way to detect both situations.

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Please explain what you mean by "inconsistencies in a set of if-then-else conditions". Without more than that cryptic description, my best guess would be that you're looking for something like a SAT solver. –  Henning Makholm Jul 20 '12 at 12:20
An example would help people to understand what you are trying to do. –  MJD Jul 20 '12 at 14:18
Sorry for being vague. I have added two examples. –  Abhishek Chanda Jul 20 '12 at 21:03
I still don't understand why if (a & b) then X and if (a & b) then Y are inconsistent. Is it because the conditions (a & b) are the same but the consequents X and Y are different? –  MJD Dec 26 '13 at 15:16