The introduction of symbols in mathematical problems eliminates the ambiguity of natural language by representing the core of the problems simply. Mathematical proofs use a chain of deduction. Despite the unique contribution of TRIZ professionals to innovative problem solving, many researchers’ effort about the development of TRIZ was based on induction rather than deduction. The Butterfly model for contradiction problem solving uses symbolic notations, and the model carries out the logical proofs of the validities of the conditional propositions by using truth tables. The Butterfly model provides the right solution strategy to solve the problems and reduces the solution space of the problems systematically. Many TRIZ researchers have argued that for a given contradiction problem, the contradiction resolution was much more innovative than any other compromise solutions which accommodated both conflicting requirements. In effect, they treated compromise-based solution strategies as naive methods. Unlike the viewpoint of the traditional TRIZ, this study suggests that the compromise is an effective alternative to solve contradictions. To prove this assertion, we firstly analyze a few contradiction problems with the Butterfly diagram. And then, we classify the types of contradiction relations and identify the conditions how the compromise approach resolves the contradiction systematically. In order to achieve the research objectives, this study explains the Butterfly model and its relevant cases.
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