Abstract
Motivated by the declarative modeling paradigm for data mining, we report on our experience in modeling and solving relational query and graph mining problems with the IDP system, a variation on the answer set programming paradigm. Using IDP or other ASP-languages for modeling appears to be natural given that they provide rich logical languages for modeling and solving many search problems and that relational query mining (and ILP) is also based on logic. Nevertheless, our results indicate that second order extensions to these languages are necessary for expressing the model as well as for efficient solving, especially for what concerns subsumption testing. We propose such second order extensions and evaluate their potential effectiveness with a number of experiments in subsumption as well as in query mining.
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A Appendix: Introduction to IDP
A Appendix: Introduction to IDP
The IDP language [1, 2] is an extension of first order logic with inductive definitions and aggregration. The IDP system implements finite satisfiability and can be considered as an ASP system.
The particular type of inference we use in our work is model expansion. The task of model expansion is to expand a finite interpretation S for the subvocabulary V of a given logic theory T to a model of T. In the example above, V is the vocabulary of the map colouring problem i.e. area, color, \(\textit{border} (\textit{area},\textit{area})\), \(\textit{coloring}::\textit{area} \mapsto \textit{color} \); S consists of 7 countries, 4 colours and a border relation between the countries; T is the constraint that two bordering countries cannot have the same color.
In this example, the model expansion task is to find an extension of S, i.e. coloring function, such that the constraint in T is satisfied, i.e. all bordering countries have different colours.
The example can be tried online (select file “Map Colouring”):
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Paramonov, S., van Leeuwen, M., Denecker, M., De Raedt, L. (2016). An Exercise in Declarative Modeling for Relational Query Mining. In: Inoue, K., Ohwada, H., Yamamoto, A. (eds) Inductive Logic Programming. ILP 2015. Lecture Notes in Computer Science(), vol 9575. Springer, Cham. https://doi.org/10.1007/978-3-319-40566-7_12
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