Towards Log-Linear Logics with Concrete Domains

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