We introduce a framework for knowledge-based sequence mining, based on Answer Set Programming (ASP). We begin by modeling the basic task and refine it in the sequel in several ways. First, we show how easily condensed patterns can be extracted by modular extensions of the basic approach. Second, we illustrate how ASP's preference handling capacities can be exploited for mining patterns of interest. In doing so, we demonstrate the ease of incorporating knowledge into the ASP-based mining process. To assess the trade-off in effectiveness, we provide an empirical study comparing our approach with a related sequence mining mechanism.