Order theoretical semantic recommendation

Mathematical concepts of order and ordering relations play multiple roles in semantic technologies. Discrete totally ordered data characterize both input streams and top-k rank-ordered recommendations and query output, while temporal attributes establish numerical total orders, either over time points or in the more complex case of start-end temporal intervals. But also of note are the fully partially ordered data, including both lattices and non-lattices, which actually dominate the semantic strcuture of ontological systems. Scalar semantic similarities over partially-ordered semantic data are traditionally used to return rank-ordered recommendations, but these require complementation with true metrics available over partially ordered sets. In this paper we report on our work in the foundations of order measurement in ontologies, with application to top-k semantic recommendation in workflows. We conclude that true ordered set metrics are strongly preferable to traditional semantic similarities.