Ontologies are the backbone of the emerging Semantic Web, which is envisioned to dramatically improve current web services by extending them with intelligent capabilities such as reasoning and context-awareness. They define a shared vocabulary of common domains accessible to both, humans and computers, and support various types of information management including storage and processing of data. Current ontology languages, which are designed to be decidable to allow for automatic data processing, target simple typed ontologies that are completely and consistently specified. As the size of ontologies and the complexity of web applications grow, the need for more flexible representation and reasoning schemes emerges. This article presents a logical framework utilizing context-dependent rules which are intended to support not fully and/or precisely specified ontologies. A hypothetical application scenario is described to illustrate the type of ontologies targeted, and the type of queries that the presented logical framework is intended to address.