  This article presents the use of Answer Set Programming (ASP) to mine
sequential patterns. ASP is a high-level declarative logic programming paradigm
for high level encoding combinatorial and optimization problem solving as well
as knowledge representation and reasoning. Thus, ASP is a good candidate for
implementing pattern mining with background knowledge, which has been a data
mining issue for a long time. We propose encodings of the classical sequential
pattern mining tasks within two representations of embeddings (fill-gaps vs
skip-gaps) and for various kinds of patterns: frequent, constrained and
condensed. We compare the computational performance of these encodings with
each other to get a good insight into the efficiency of ASP encodings. The
results show that the fill-gaps strategy is better on real problems due to
lower memory consumption. Finally, compared to a constraint programming
approach (CPSM), another declarative programming paradigm, our proposal showed
comparable performance.
