Distributed reasoning in M2M leverages the expressive power of ontology to enable semantic interoperability between heterogeneous systems of connected devices. Ontology, however, lacks the built-in, principled support to effectively handle the uncertainty inherent in M2M application domains. Thus, efficient reasoning can be achieved by integrating the inferential reasoning power of probabilistic representations with the first-order expressiveness of ontology. But there remains a gap with current probabilistic ontologies since state-of-the-art provides no compatible representation for simultaneous handling of discrete and continuous quantities in ontology. This requirement is paramount, especially in smart homes, where continuous quantities cannot be avoided, and simply mapping continuous information to discrete states through quantization can cause a great deal of information loss. In this paper, we propose a hybrid probabilistic ontology that can simultaneously handle distributions over discrete and continuous quantities in ontology. We call this new framework HyProb-Ontology, and it specifies distributions over properties of classes, which serve as templates for instances of classes to inherit as well as overwrite some aspects. Since there cannot be restriction on the dependency topology of models that HyProb-Ontology can induce across different domains, we can achieve a unified Ground Hybrid Probabilistic Model by conditional Gaussian fuzzification of the distributions of the continuous variables in ontology. From the results of our experiments, this unified model can achieve exact inference with better performance over classical Bayesian networks.
