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Reasoning with Qualitative Velocity: Towards a Hybrid Approach

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Book cover Hybrid Artificial Intelligent Systems (HAIS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7208))

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Abstract

Qualitative description of the movement of objects can be very important when there are large quantity of data or incomplete information, such as in positioning technologies and movement of robots. We present a first step in the combination of fuzzy qualitative reasoning and quantitative data obtained by human interaction and external devices as GPS, in order to update and correct the qualitative information. We consider a Propositional Dynamic Logic which deals with qualitative velocity and enables us to represent some reasoning tasks about qualitative properties. The use of logic provides a general framework which improves the capacity of reasoning. This way, we can infer additional information by using axioms and the logic apparatus. In this paper we present sound and complete relational dual tableau that can be used for verification of validity of formulas of the logic in question.

Partially supported by projects TIN2006-15455-C03-01 and P6-FQM-02049.

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References

  1. Abraham, A., Corchado, E., Corchado, J.M.: Hybrid learning machines. Neurocomputing 72(13-15), 2729–2730 (2009)

    Article  Google Scholar 

  2. Bennett, B., Cohn, A., Wolter, A., Zakharyaschev, M.: Multi-dimensional modal logic as a framework for spatio-temporal reasoning. Applied Intelligence 17(3), 239–251 (2002)

    Article  MATH  Google Scholar 

  3. Burrieza, A., Muñoz-Velasco, E., Ojeda-Aciego, M.: A PDL approach for qualitative velocity. Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems 19(01), 11–26 (2011)

    Article  MATH  Google Scholar 

  4. Burrieza, A., Muñoz-Velasco, E., Ojeda-Aciego, M.: Closeness and Distance Relations in Order of Magnitude Qualitative Reasoning via PDL. In: Meseguer, P., Mandow, L., Gasca, R.M. (eds.) CAEPIA 2009. LNCS(LNAI), vol. 5988, pp. 71–80. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  5. Burrieza, A., Ojeda-Aciego, M., Orłowska, E.: An implementation of a dual tableaux system for order-of-magnitude qualitative reasoning. International Journal of Computer Mathematics 86, 1852–1866 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cohn, A., Renz, J.: Handbook of Knowledge Representation. Elsevier (2007)

    Google Scholar 

  7. Corchado, E., Abraham, A., de Carvalho, A.: Editorial: Hybrid intelligent algorithms and applications. Information Science 180, 2633–2634 (2010)

    Article  Google Scholar 

  8. Corchado, E., Graña, M., Wozniak, M.: New trends and applications on hybrid artificial intelligence systems. Neurocomputing 75(1), 61–63 (2012)

    Article  Google Scholar 

  9. Delafontaine, M., Bogaert, P., Cohn, A.G., Witlox, F., Maeyer, P.D., de Weghe, N.V.: Inferring additional knowledge from QTC N relations. Information Sciences (2011), doi:10.1016/j.ins.2010.12.021

    Google Scholar 

  10. Duckham, M., Lingham, J., Mason, K., Worboys, M.: Qualitative reasoning about consistency in geographic information. Information Sciences 176(6), 601–627 (2006)

    Article  Google Scholar 

  11. Escrig, M.T., Toledo, F.: Qualitative Velocity. In: Escrig, M.T., Toledo, F.J., Golobardes, E. (eds.) CCIA 2002. LNCS (LNAI), vol. 2504, pp. 28–39. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  12. Faltings, B.: A symbolic approach to qualitative kinematics. Artificial Intelligence 56(2-3), 139–170 (1992)

    Article  MathSciNet  Google Scholar 

  13. Forbus, K., Nielsen, P., Faltings, B.: Qualitative kinematics: A framework. In: Proceedings of the Int. Joint Conference on Artificial Intelligence, pp. 430–437 (1987)

    Google Scholar 

  14. García, S., Fernández, A., Luengo, J., Herrera, F.: Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: Experimental analysis of power. Information Sciences 180(10), 2044–2064 (2010)

    Article  Google Scholar 

  15. Golińska-Pilarek, J., Mora, A., Muñoz-Velasco, E.: An ATP of a Relational Proof System for Order of Magnitude Reasoning with Negligibility, Non-closeness and Distance. In: Ho, T.-B., Zhou, Z.-H. (eds.) PRICAI 2008. LNCS (LNAI), vol. 5351, pp. 128–139. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  16. Golińska-Pilarek, J., Muñoz-Velasco, E.: Dual tableau for a multimodal logic for order of magnitude qualitative reasoning with bidirectional negligibility. International Journal of Computer Mathematics 86, 1707–1718 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  17. Hinrichs, T., Forbus, K., de Kleer, J., Yoon, S., Jones, E., Hyland, R., Wilson, J.: Hybrid Qualitative Simulation of Military Operations. In: Proc. Twenty-Third IAAI Conf. (2011)

    Google Scholar 

  18. Liu, W., Li, S., Renz, J.: Combining RCC-8 with qualitative direction calculi: Algorithms and complexity. In: Proceedings of IJCAI 2009, pp. 854–859 (2009)

    Google Scholar 

  19. Liu, H., Brown, D.J., Coghill, G.M.: Fuzzy qualitative robot kinematics. IEEE Transactions on Fuzzy Systems 16(3), 808–822 (2008)

    Article  Google Scholar 

  20. Miene, A., Visser, U., Herzog, O.: Recognition and Prediction of Motion Situations Based on a Qualitative Motion Description. In: Polani, D., Browning, B., Bonarini, A., Yoshida, K. (eds.) RoboCup 2003. LNCS (LNAI), vol. 3020, pp. 77–88. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  21. Nielsen, P.: A qualitative approach to rigid body mechanics, University of Illinois at Urbana-Champaign, PhD thesis (1988)

    Google Scholar 

  22. Orłowska, E., Golińska-Pilarek, J.: Dual Tableaux: Foundations, Methodology, Case Studies. Trends in Logic, vol. 36. Springer Science (2011)

    Google Scholar 

  23. Pedrycz, W., Aliev, R.: Logic-oriented neural networks for fuzzy neurocomputing. Neurocomputing 73(1-3), 10–23 (2009)

    Article  Google Scholar 

  24. Randell, D., Cui, Z., Cohn, A.: A spatial logic based on regions and connection. In: Proceedings of KR, pp. 165–176 (1992)

    Google Scholar 

  25. Rasiowa, H., Sikorski, R.: On gentzen theorem. Fund. Mathematicae 48, 57–69 (1960)

    MathSciNet  MATH  Google Scholar 

  26. Roduit, P., Martinoli, A., Jacot, J.: A quantitative method for comparing trajectories of mobile robots using point distribution models. In: Proc. Intelligent Robots and Systems, IROS 2007, pp. 2441–2448 (2007)

    Google Scholar 

  27. Sokolsky, O., Hong, H.S.: Qualitative modeling of hybrid systems. In: Proc. of the Montreal Workshop (2001), http://www.cis.upenn.edu/~rtg/rtg_papers.html

  28. Stolzenburg, F., Obst, O., Murray, J.: Qualitative Velocity and Ball Interception. In: Jarke, M., Koehler, J., Lakemeyer, G. (eds.) KI 2002. LNCS (LNAI), vol. 2479, pp. 283–298. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  29. Tarski, A.: On the calculus of relations. Journal of Symbolic Logic 6, 73–89 (1941)

    Article  MathSciNet  MATH  Google Scholar 

  30. Van de Weghe, N., Kuijpers, B., Bogaert, P., De Maeyer, P.: A Qualitative Trajectory Calculus and the Composition of Its Relations. In: Rodríguez, M.A., Cruz, I., Levashkin, S., Egenhofer, M. (eds.) GeoS 2005. LNCS, vol. 3799, pp. 60–76. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  31. Vries, D., Verheijen, P.J.T., den Dekker, A.J.: Hybrid system modeling and identification of cell biology systems: perspectives and challenges. In: Proc. 15th IFAC Symposium on System Identification, pp. 227–232 (2009)

    Google Scholar 

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Golińska-Pilarek, J., Muñoz-Velasco, E. (2012). Reasoning with Qualitative Velocity: Towards a Hybrid Approach. In: Corchado, E., Snášel, V., Abraham, A., Woźniak, M., Graña, M., Cho, SB. (eds) Hybrid Artificial Intelligent Systems. HAIS 2012. Lecture Notes in Computer Science(), vol 7208. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28942-2_57

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  • DOI: https://doi.org/10.1007/978-3-642-28942-2_57

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28941-5

  • Online ISBN: 978-3-642-28942-2

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