Logical inference, an integral feature of the Semantic Web, is the process of deriving new triples by applying entailment rules on knowledge bases. The entailment rules are determined by the model-theoretic semantics. Incorporating context of an RDF triple (e.g., provenance, time, and location) into the inferencing process requires the formal semantics to be capable of describing the context of RDF triples also in the form of triples, or in other words, RDF contextual triples about triples. The formal semantics should also provide the rules that could entail new contextual triples about triples. In this paper, we propose the first inferencing mechanism that allows context of RDF triples, represented in the form of RDF triples about triples, to be the first-class citizens in the model-theoretic semantics and in the logical rules. Our inference mechanism is well-formalized with all new concepts being captured in the model-theoretic semantics. This formal semantics also allows us to derive a new set of entailment rules that could entail new contextual triples about triples. To demonstrate the feasibility and the scalability of the proposed mechanism, we implement a new tool in which we transform the existing knowledge bases to our representation of RDF triples about triples and provide the option for this tool to compute the inferred triples for the proposed rules. We evaluate the computation of the proposed rules on a large scale using various real-world knowledge bases such as Bio2RDF NCBI Genes and DBpedia. The results show that the computation of the inferred triples can be highly scalable. On average, one billion inferred triples adds 5-6 minutes to the overall transformation process. NCBI Genes, with 20 billion triples in total, took only 232 minutes for the transformation of 12 billion triples and added 42 minutes for inferring 8 billion triples to the overall process.