Many statements in the massive scientific text data are in the form of conditional sentences. Conditions are of great importance to facts. Existing conditional knowledge graphs have introduced condition triples, but ignore the latent semantic relations between fact and condition triples and the logical relationships among condition triples. To address these issues, we propose a novel conditional knowledge graph representation, which is a nested hierarchical triple. We design a new extraction strategy that employs a text hierarchy parsing module to extract the semantic relations between facts and conditions and a triple extraction module to extract fact and condition triples. Moreover, we provide a corresponding knowledge storage scheme which can store conditional knowledge. Experimental results on our constructed conditional dataset show that our model can not only capture semantic relations between fact and condition triples as well as logical relationships among condition triples, but also significantly improve the accuracy of triple extractions compared to baselines.