Document Open Access Logo

Extracting Interval Temporal Logic Rules: A First Approach

Authors Davide Bresolin , Enrico Cominato, Simone Gnani, Emilio Muñoz-Velasco , Guido Sciavicco

Thumbnail PDF


  • Filesize: 430 kB
  • 15 pages

Document Identifiers

Author Details

Davide Bresolin
  • Department of Mathematics, University of Padova, Italy
Enrico Cominato
  • Department of Mathematics, Computer Science and Physics, University of Udine, Italy
Simone Gnani
  • Department of Mathematics and Computer Science, University of Ferrara, Italy
Emilio Muñoz-Velasco
  • Department of Applied Mathematics, University of Malaga, Spain
Guido Sciavicco
  • Department of Mathematics and Computer Science, University of Ferrara, Italy

Cite AsGet BibTex

Davide Bresolin, Enrico Cominato, Simone Gnani, Emilio Muñoz-Velasco, and Guido Sciavicco. Extracting Interval Temporal Logic Rules: A First Approach. In 25th International Symposium on Temporal Representation and Reasoning (TIME 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 120, pp. 7:1-7:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


Discovering association rules is a classical data mining task with a wide range of applications that include the medical, the financial, and the planning domains, among others. Modern rule extraction algorithms focus on static rules, typically expressed in the language of Horn propositional logic, as opposed to temporal ones, which have received less attention in the literature. Since in many application domains temporal information is stored in form of intervals, extracting interval-based temporal rules seems the natural choice. In this paper we extend the well-known algorithm APRIORI for rule extraction to discover interval temporal rules written in the Horn fragment of Halpern and Shoham's interval temporal logic.

Subject Classification

ACM Subject Classification
  • Information systems → Clustering and classification
  • Interval temporal logic
  • Horn fragment
  • Rule extraction


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. L. Aceto, D. Della Monica, V. Goranko, A. Ingólfsdóttir, A. Montanari, and G. Sciavicco. A complete classification of the expressiveness of interval logics of Allen’s relations: the general and the dense cases. Acta Informatica, 53(3):207-246, 2016. Google Scholar
  2. R. Agrawal, T. Imieliński, and A. N. Swami. Mining association rules between sets of items in large databases. In Proc. of the 1993 ACM SIGMOD International Conference on Management of Data, pages 207-216, 1993. Google Scholar
  3. R. Agrawal and R. Srikant. Mining sequential patterns. In Proc. of the 11th International Conference on Data Engineering, pages 3-14, 1995. Google Scholar
  4. J.F. Allen. Maintaining knowledge about temporal intervals. Communications of the ACM, 26(11):832-843, 1983. Google Scholar
  5. R. Alluhaibi. Simple interval temporal logic for natural language assertion descriptions. In Proc. of the 11th International Conference on Computational Semantics, pages 283-293, 2015. Google Scholar
  6. R.A. Baeza-Yates. Challenges in the interaction of information retrieval and natural language processing. In Proc. of the 5th International on Computational Linguistics and Intelligent Text Processing (CICLing), pages 445-456, 2004. Google Scholar
  7. L. Bozzelli, A. Molinari, A. Montanari, A. Peron, and P. Sala. Satisfiability and model checking for the logic of sub-intervals under the homogeneity assumption. In Proc. of the 44th International Colloquium on Automata, Languages, and Programming, pages 120:1-120:14, 2017. Google Scholar
  8. D. Bresolin, D. Della Monica, A. Montanari, and G. Sciavicco. The light side of interval temporal logic: the Bernays-Schönfinkel fragment of CDT. Annals of Mathematics and Artificial Intelligence, 71(1-3):11-39, 2014. Google Scholar
  9. D. Bresolin, A. Kurucz, E. Muñoz-Velasco, V. Ryzhikov, G. Sciavicco, and M. Zakharyaschev. Horn fragments of the Halpern-Shoham interval temporal logic. ACM Transactions on Computational Logic, 18(3):22:1-22:39, 2017. Google Scholar
  10. D. Bresolin, D. Della Monica, A. Montanari, P. Sala, and G. Sciavicco. Interval temporal logics over strongly discrete linear orders: Expressiveness and complexity. Theoretical Compututer Science, 560:269-291, 2014. Google Scholar
  11. D. Bresolin, E. Muñoz-Velasco, and G. Sciavicco. Fast(er) reasoning in interval temporal logic. In Proc. of the 26th Annual Conference on Computer Science Logic, volume 82 of LIPIcs, pages 17:1-17:17. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2017. Google Scholar
  12. C. Combi, M. Mantovani, and P. Sala. Discovering quantitative temporal functional dependencies on clinical data. In Proc. of the 2017 IEEE International Conference on Healthcare Informatics, pages 248-257, 2017. Google Scholar
  13. C. Combi and P. Sala. Mining approximate interval-based temporal dependencies. Acta Informatica, 53(6-8):547-585, 2016. Google Scholar
  14. P. Cotofrei and K. Stoffel. Classification rules + time = temporal rules. In Proc. of the 2002 International Conference on Computational Science, pages 572-581, 2002. Google Scholar
  15. S. de Amo, D. A. Furtado, A. Giacometti, and D. Laurent. An apriori-based approach for first-order temporal pattern. Journal of Information and Data Management, 1(1):57-70, 2010. Google Scholar
  16. J. Fürnkranz, D. Gamberger, and N. Lavrac. Foundations of Rule Learning. Cognitive Technologies. Springer, 2012. Google Scholar
  17. J. Fürnkranz and T. Kliegr. A brief overview of rule learning. In Proc. of the 9th International Symposium Rule Technologies: Foundations, Tools, and Applications, pages 54-69, 2015. Google Scholar
  18. Leslie Ann Goldberg. Efficient Algorithms for Listing Combinatorial Structures. Distinguished Dissertations in Computer Science. Cambridge University Press, New York, NY, USA, 1993. Google Scholar
  19. J.Y. Halpern and Y. Shoham. A propositional modal logic of time intervals. Journal of the ACM, 38(4):935-962, 1991. Google Scholar
  20. J. Han, J. Pei, Y. Yin, and R. Mao. Mining frequent patterns without candidate generation: A frequent-pattern tree approach. Data Mining and Knowledge Discovery, 8(1):53-87, 2004. Google Scholar
  21. F. Jiménez, G. Sánchez, and J.M. Juárez. Multi-objective evolutionary algorithms for fuzzy classification in survival prediction. Artificial Intelligence in Medicine, 60(3):197-219, 2014. Google Scholar
  22. David S. Johnson, Mihalis Yannakakis, and Christos H. Papadimitriou. On generating all maximal independent sets. Information Processing Letters, 27(3):119-123, 1988. Google Scholar
  23. W.A. Kosters, W. Pijls, and V. Popova. Complexity analysis of depth first and fp-growth implementations of APRIORI. In Proc. of the 3rd International Conference on Machine Learning and Data Mining in Pattern Recognition, pages 284-292, 2003. Google Scholar
  24. Z. Michalewicz. Genetic algorithms + data structures = evolution programs. Artificial Intelligence. Springer, 1992. Google Scholar
  25. A. Molinari, A. Montanari, A. Murano, G. Perelli, and A. Peron. Checking interval properties of computations. Acta Informatica, 53(6-8):587-619, 2016. Google Scholar
  26. D. Della Monica, D. de Frutos-Escrig, A. Montanari, A. Murano, and G. Sciavicco. Evaluation of temporal datasets via interval temporal logic model checking. In Proc. of the 24th International Symposium on Temporal Representation and Reasoning, volume 90 of LIPIcs, pages 11:1-11:18. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2017. Google Scholar
  27. A. Montanari, I. Pratt-Hartmann, and P. Sala. Decidability of the logics of the reflexive sub-interval and super-interval relations over finite linear orders. In Proc. of the 17th International Symposium on Temporal Representation and Reasoning, pages 27-34. IEEE Computer Society, 2010. Google Scholar
  28. A. Montanari, G. Puppis, and P. Sala. Maximal decidable fragments of Halpern and Shoham’s modal logic of intervals. In Proc. of the 37th International Colloquium on Automata, Languages and Programming, volume 6199 of LNCS, pages 345-356. Springer, 2010. Google Scholar
  29. S. Muggleton. Inductive logic programming: Issues, results and the challenge of learning language in logic. Artificial Intelligence, 114(1-2):283-296, 1999. Google Scholar
  30. E. Muñoz-Velasco, M. Pelegrín-García, P. Sala, and G. Sciavicco. On coarser interval temporal logics and their satisfiability problem. In Proc. of the 16th Conference of the Spanish Association for Artificial Intelligence, volume 9422 of LNCS, pages 105-115. Springer, 2015. Google Scholar
  31. I. Pratt-Hartmann. Temporal prepositions and their logic. Artificial Intelligence, 166(1-2):1-36, 2005. Google Scholar
  32. L. De Raedt. Logical and relational learning. Cognitive Technologies. Springer, 2008. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail