Using SPARQL to Test for Lattices: application to quality assurance in biomedical ontologies.

We present a scalable, SPARQL-based computational pipeline for testing the lattice-theoretic properties of partial orders represented as RDF triples. The use case for this work is quality assurance in biomedical ontologies, one desirable property of which is conformance to lattice structures. At the core of our pipeline is the algorithm called NuMi, for detecting the Number of Minimal upper bounds of any pair of elements in a given finite partial order. Our technical contribution is the coding of NuMi completely in SPARQL. To show its scalability, we applied NuMi to the entirety of SNOMED CT, the largest clinical ontology (over 300,000 conepts). Our experimental results have been groundbreaking: for the first time, all non-lattice pairs in SNOMED CT have been identified exhaustively from 34 million candidate pairs using over 2.5 billion queries issued to Virtuoso. The percentage of non-lattice pairs ranges from 0 to 1.66 among the 19 SNOMED CT hierarchies. These non-lattice pairs represent target areas for focused curation by domain experts. RDF, SPARQL and related tooling provide an e cient platform for implementing lattice algorithms on large data structures.