The 3D Semantic Annotation (3DSA) system expedites the classification of 3D digital surrogates from the cultural heritage domain, by leveraging crowd-sourced semantic annotations. More specifically, the 3DSA system generates high-level classifications of 3D objects by applying rule-based reasoning across community-generated annotations and low-level shape and size attributes. This paper describes a particular use of the 3DSA system – cataloguing Greek pottery. It also describes our novel approach to rule-based reasoning that is modelled on concepts inspired from Markov logic networks. Our evaluation of this approach demonstrates its efficiency, accuracy and versatility, compared to classical rule-based reasoning.