The search engine has become one of the most popular tools used on the Internet. Most of the existing search engines locate information based on queries consisting of a small number of keywords provided by the users. Although those search engines can query their databases and retrieve documents in a timely manner, the quality of the results is often unsatisfactory. This problem, based on previous studies and our observation, is partially due to the lack of semantic interpretation of a search request, as well as the user's incapability to precisely express their information need in a short query. In this research, we propose a conceptual framework that classifies various types of context in a Web search environment and present a new semantics-based approach that disambiguates user queries by analyzing the "relationship" context associated with query concepts.Our multi-methodological research approach includes: (i) building a context framework by categorizing different types of context; (ii) proposing a search mechanism that discovers and utilizes semantic relationships among query terms; (iii) demonstrating the practical implications of our proposed model using a proof-of-concept prototype system; and (iv) evaluating the usefulness of "relationship" context through an experimental study. From a technical perspective, our approach integrates ideas from semantic network, ontology, and information retrieval techniques. The experimental study conducted in the medical domain shows that our approach is effective and outperforms an existing popular search engine on search tasks consisting of key semantic relationships.