The Semantic Web is a distributed environment for knowledge representation and reasoning. The distributed nature brings with it failing data sources and inconsistencies between autonomous knowledge bases. To reduce problems resulting from unavailable sources and to improve performance, caching can be used. Caches, however, raise new problems of imprecise or outdated information. We propose to distinguish between certain and cached information when reasoning on the semantic web, by extending the well known $\mathcal{FOUR}$ bilattice of truth and knowledge orders to $\mathcal{FOUR-C}$ , taking into account cached information. We discuss how users can be offered additional information about the reliability of inferred information, based on the availability of the corresponding information sources. We then extend the framework towards $\mathcal{FOUR-T}$ , allowing for multiple levels of trust on data sources. In this extended setting, knowledge about trust in information sources can be used to compute, how well an inferred statement can be trusted and to resolve inconsistencies arising from connecting multiple data sources. We redefine the stable model and well founded semantics on the basis of $\mathcal{FOUR-T}$ , and reformalize the Web Ontology Language OWL2 based on logical bilattices, to augment OWL knowledge bases with trust based reasoning.