Information exploration processes are usually recognized by their inherent complexity, lack of knowledge and uncertainty, concerning both the domain and the solution strategies. Even though there has been much work on the development of computational systems supporting exploration tasks, such as faceted search and set-oriented interfaces, the lack of a formal understanding of the exploration process and the absence of a proper separation of concerns approach in the design phase is the cause of many expressivity issues and serious limitations. This work proposes a novel design approach of exploration tools based on a formal framework for representing exploration actions and processes. Moreover, we present a new exploration system that generalizes the majority of the state-of-the art exploration tools. The evaluation of the proposed framework is guided by case studies and comparisons with state-of-the-art tools. The results show the relevance of our approach both for the design of new exploration tools with higher expressiveness, and formal assessments and comparisons between different tools.