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Fast(er) Reasoning in Interval Temporal Logic

Authors Davide Bresolin, Emilio Muñoz-Velasco, Guido Sciavicco

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Davide Bresolin
Emilio Muñoz-Velasco
Guido Sciavicco

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Davide Bresolin, Emilio Muñoz-Velasco, and Guido Sciavicco. Fast(er) Reasoning in Interval Temporal Logic. In 26th EACSL Annual Conference on Computer Science Logic (CSL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 82, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.CSL.2017.17

Abstract

Clausal forms of logics are of great relevance in Artificial Intelligence, because they couple a high expressivity with a low complexity of reasoning problems. They have been studied for a wide range of classical, modal and temporal logics to obtain tractable fragments of intractable formalisms. In this paper we show that such restrictions can be exploited to lower the complexity of interval temporal logics as well. In particular, we show that for the Horn fragment of the interval logic AAbar (that is, the logic with the modal operators for Allen’s relations meets and met by) without diamonds the complexity lowers from NEXPTIME-complete to P-complete. We prove also that the tractability of the Horn fragments of interval temporal logics is lost as soon as other interval temporal operators are added to AAbar, in most of the cases.

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Keywords
  • Temporal Logic
  • Horn Fragments
  • Satisfiability
  • Complexity

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References

  1. J. F. Allen. Maintaining knowledge about temporal intervals. Communications of the ACM, 26(11):832-843, 1983. Google Scholar
  2. J. F. Allen. Towards a general theory of action and time. Artificial Intelligence, 23(2):123-154, 1984. Google Scholar
  3. D. Anicic, P. Fodor, N. Stojanovic, and R. Stühmer. Computing complex events in an event-driven and logic-based approach. In Proc. of the 3rd ACM International Conference on Distributed Event-Based Systems (DEBS), pages 1-2, 2009. Google Scholar
  4. A. Artale, R. Kontchakov, V. Ryzhikov, and M. Zakharyaschev. The complexity of clausal fragments of LTL. In Proc. of the 19th International Conference Logic for Programming, Artificial Intelligence, and Reasoning (LPAR), pages 35-52, 2013. Google Scholar
  5. A. Artale, R. Kontchakov, V. Ryzhikov, and M. Zakharyaschev. A cookbook for temporal conceptual data modelling with description logics. ACM Transactions on Computational Logic, 15(3):1-50, 2014. Google Scholar
  6. A. Artale, R. Kontchakov, V. Ryzhikov, and M. Zakharyaschev. Tractable interval temporal propositional and description logics. In Proc. of the 29th AAAI Conference on Artificial Intelligence (AAAI), pages 1417-1423, 2015. Google Scholar
  7. B. Aspvall, M. F. Plass, and R. E. Tarjan. A linear time algorithm for testing the truth of certain quantified boolean formulas. Information Processing Letters, 8(3):121-123, 1979. Google Scholar
  8. 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, 2017. in press. Google Scholar
  9. D. Bresolin, D. Della Monica, A. Montanari, P. Sala, and G. Sciavicco. Interval temporal logics over strongly discrete linear orders: Expressiveness and complexity. Theoretical Computer Science, 560:269-291, 2014. Google Scholar
  10. D. Bresolin, A. Montanari, and P. Sala. An optimal tableau-based decision algorithm for Propositional Neighborhood Logic. In Proc. of the 24th International Symposium on Theoretical Aspects of Computer Science (STACS), volume 4393 of LNCS, pages 549-560. Springer, 2007. Google Scholar
  11. D. Bresolin, E. Muñoz-Velasco, and G. Sciavicco. Sub-propositional fragments of the interval temporal logic of Allen’s relations. In Proc. of the 14th European Conference on Logics in Artificial Intelligence (JELIA), volume 8761 of LNCS, pages 122-136, 2014. Google Scholar
  12. D. Bresolin, E. Muñoz-Velasco, and G. Sciavicco. On the complexity of fragments of horn modal logics. In Proc. of the 23rd International Symposium on Temporal Representation and Reasoning, (TIME), pages 186-195, 2016. Google Scholar
  13. D. Bresolin, E. Muñoz-Velasco, and G. Sciavicco. On the expressive power of sub-propositional fragments of modal logic. In Proc. of the 7th International Symposium on Games, Automata, Logics and Formal Verification (GandALF), pages 91-104, 2016. Google Scholar
  14. C. C. Chen and I. P. Lin. The computational complexity of satisfiability of temporal Horn formulas in propositional linear-time temporal logic. Information Processing Letters, 45(3):131-136, 1993. Google Scholar
  15. C. C. Chen and I. P. Lin. The computational complexity of the satisfiability of modal Horn clauses for modal propositional logics. Theoretical Computer Science Comput, 129(1):95-121, 1994. Google Scholar
  16. L. Fariñas Del Cerro and M. Penttonen. A note on the complexity of the satisfiability of modal Horn clauses. Journal of Logic Programming, 4(1):1-10, 1987. Google Scholar
  17. J. Y. Halpern and Y. Shoham. A propositional modal logic of time intervals. Journal of the ACM, 38(4):935-962, 1991. Google Scholar
  18. A. Horn. On sentences which are true of direct unions of algebras. Journal of Symbolic Logic, 16(1):14-21, 1951. Google Scholar
  19. S. B. Kotsiantis. Supervised machine learning: A review of classification techniques. In Proc. of the 2007 Conference on Emerging Artificial Intelligence Applications in Computer Engineering, pages 3-24, 2007. Google Scholar
  20. M. R. Krom. The decision problem for formulas in prenex conjunctive normal form with binary disjunction. Journal of Symbolic Logic, 35(2):14-21, 1970. Google Scholar
  21. L. Rokachand O. Maimon. Data Mining with Decision Trees: Theory and Applications. World Scientific Publishing Co., Inc., 2008. Google Scholar
  22. L. A. Nguyen. On the complexity of fragments of modal logics. Advances in Modal Logic, 5:318-330, 2004. Google Scholar
  23. C. H. Papadimitriou. Computational Complexity. Wiley, 2003. Google Scholar
  24. V. Radhakrishna, P. V. Kumar, and V. Janaki. A survey on temporal databases and data mining. In Proc. of the International Conference on Engineering (MIS), pages 1-6. ACM, 2015. Google Scholar
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