One strategy for building ontologies covering domains such as disease or anatomy is to weave together existing knowledge sources (databases, vocabularies and ontologies) into single cohesive whole. A first step in this process is to generate mappings between the elements of these different sources. There are a number of well-known techniques for generating mappings, both manual and automatic. Sometimes mappings are seen as an end in themselves, with the sources remaining in a loosely connected state. However, if we want to take the next step and use the mappings to weave together the different sources into a cohesive reference ontology, then we need to translate the mappings into precise logical relationships. This will allow us to safely merge equivalent concepts, creating a unified ontology. This translation is a non-trivial step, as each mapping can be interpreted as multiple different logical relationships, with each interpretation affecting the likelihood of the others. There is a lack of automated methods to assist with this last step; this resolution is typically performed by expert ontologists. Here we describe an ontology construction technique that takes two or more ontologies linked by hypothetical axioms, and estimates the most likely unified logical ontology. Hypothetical axioms can themselves be derived from semantically loose mappings. The method combines deductive reasoning and probabilistic inference and is called Bayesian OWL Ontology Merging (BOOM). We describe a special form k-BOOM that works by factorizing the probabilistic ontology into k submodules. We also briefly describe a supplemental lexical and knowledge-based technique for generating a set of hypothetical axioms from loose mappings. We are currently using this technique to build a merged disease ontology (Monarch Disease Ontology; MonDO) that unifies a broad range of vocabularies into a consistent and coherent whole.
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