Answer set programming (ASP) is a popular declarative programming paradigm with a wide range of applications in artificial intelligence. Oftentimes, when modeling an AI problem with ASP, and in particular when we are interested beyond simple search for optimal solutions, an actual solution, differences between solutions, or number of solutions of the ASP program matter. For example, when a user aims to identify a specific answer set according to her needs, or requires the total number of diverging solutions to comprehend probabilistic applications such as reasoning in medical domains. Then, there are only certain problem specific and handcrafted encoding techniques available to navigate the solution space of ASP programs, which is oftentimes not enough. In this paper, we propose a formal and general framework for interactive navigation toward desired subsets of answer sets analogous to faceted browsing. Our approach enables the user to explore the solution space by consciously zooming in or out of sub-spaces of solutions at a certain configurable pace. We illustrate that weighted faceted navigation is computationally hard. Finally, we provide an implementation of our approach that demonstrates the feasibility of our framework for incomprehensible solution spaces.