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.

Many knowledge representation tasks involve trees or similar structures as abstract datatypes.  However, devising compact and efficient declarative representations of such properties is non-obvious and can be challenging indeed.  In this paper, we take acyclicity properties into consideration and investigate logic-based approaches to encode them.  We use answer set programming as the primary representation language but also consider mappings to related formalisms, such as propositional logic, difference logic, and linear programming.