In this paper, we present a new method for propositionalization that works in a bottom-up, data-driven manner. It is tailored for biochemical databases, where the examples are 2-D descriptions of chemical compounds. The method generates all frequent fragments (i.e., linearly connected atoms) up to a user-specified length. A preliminary experiment in the domain of carcinogenicity predictions showed that bottom-up propositionalization is a promising approach to feature construction from relational data.