We present a computational framework for conceptual blending, a concept invention method that is advocated in cognitive science as a fundamental and uniquely human engine for creative thinking. Our framework treats a crucial part of the blending process, namely the generalisation of input concepts, as a search problem that is solved by means of modern answer set programming methods to find commonalities among input concepts. We also address the problem of pruning the space of possible blends by introducing metrics that capture most of the so-called optimality principles, described in the cognitive science literature as guidelines to produce meaningful and serendipitous blends. As a proof of concept, we demonstrate how our system invents novel concepts and theories in domains where creativity is crucial, namely mathematics and music.