Many dynamic analysis approaches to specification mining, which extract behavioral models from execution traces, do not consider object identities. This limits their power when used to analyze traces of general object oriented programs. In this work we present a novel specification mining approach that considers object identities, and, moreover, generalizes from specifications involving concrete objects to their symbolic class-level abstractions. Our approach uses data mining methods to extract significant scenario-based specifications in the form of Damm and Harel's live sequence charts (LSC), a formal and expressive extension of classic sequence diagrams. We guarantee that all mined symbolic LSCs are significant (statistically sound) and all significant symbolic LSCs are mined (statistically complete). The technique can potentially be applied to general object oriented programs to reveal expressive and useful reverse-engineered candidate specifications.