Towards Log-Linear Logics with Concrete Domains

We present ${\mathcal{M}\mathcal{E}\mathcal{L}}^{++}$ (M denotes Markov logic networks) an extension of the log-linear description logics ${\mathcal{E}\mathcal{L}}^{++}$-LL with concrete domains, nominals, and instances. We use Markov logic networks (MLNs) in order to find the most probable, classified and coherent ${\mathcal{E}\mathcal{L}}^{++}$ ontology from an ${\mathcal{M}\mathcal{E}\mathcal{L}}^{++}$ knowledge base. In particular, we develop a novel way to deal with concrete domains (also known as datatypes) by extending MLN’s cutting plane inference (CPI) algorithm.