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Agents’ Logics with Common Knowledge and Uncertainty: Unification Problem, Algorithm for Construction Solutions

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Book cover Knowledge-Based and Intelligent Information and Engineering Systems (KES 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6881))

Abstract

This paper studies agents’ logics with operation uncertainty. Prime attention is paid to agents’ common knowledge logics with logical operation uncertainty and logical unification in these logics. The unification problem is: for two arbitrary given formulas with meta-variables (coefficients) to answer whether they are unifiable, and if yes to construct a unifier. This problem is equivalent to problem of solvability logical equations with coefficients and finding theirs solutions. We show that the basic common knowledge logic with uncertainty operation (notation - CKL n,U ) is decidable w.r.t. logical unification of the common knowledge formulas, and that for unifiable common knowledge formulas we can construct a unifier (we may describe solving algorithm). This result is extended to a wide class of logics expanding CKL n,U .

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References

  1. Baader, F., Narendran, P.: Unification of Concept Terms in Description Logics. J. Symbolic Computation 31(3), 257–305 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  2. Baader, F., Küsters, R.: Unification in Description Logics with Transitive Closure of Roles. In: Nieuwenhuis, R., Voronkov, A. (eds.) LPAR 2001. LNCS (LNAI), vol. 2250, pp. 217–232. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  3. Baader, F., Snyder, W.: Unification Theory. In: Handbook of Automated Reasoning, pp. 445–532 (2001)

    Google Scholar 

  4. Baader, F., Morawska, B.: Unification in the Description Logic EL. In: Treinen, R. (ed.) RTA 2009. LNCS, vol. 5595, pp. 350–364. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  5. Baader, F., Ghilardi, S.: Unification in modal and description logics. Logic J. of IGPL (2010); First published online (April 29, 2010), doi:10.1093/jigpal/jzq008

    Google Scholar 

  6. Brachman, R.J., Schmolze, J.G.: An overview on the KL-ONE knowledge representation system. Cognitive Science 9(2), 179–226 (1985)

    Article  Google Scholar 

  7. Barwise, J.: Three Views of Common Knowledge. In: Vardi (ed.) Proc. Second Confeuence on Theoretical Aspects of Reasoning about Knowledge, pp. 365–379. Morgan Kaufmann, San Francisco (1988)

    Google Scholar 

  8. Dwork, C., Moses, Y.: Knowledge and Common Knowledge in a Byzantine Environment: Crash Failures. Information and Computation 68(2), 156–183 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  9. Ghilardi, S.: Unification, finite duality and projectivity in varieties of Heyting algebras. Ann. Pure Appl. Logic 127(1-3), 99–115 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ghilardi, S., Sacchetti, L.: Filtering unification and most general unifiers in modal logic. J. Symb. Log. 69(3), 879–906 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  11. Ghilardi, S.: Best Solving Modal Equations. Ann. Pure Appl. Logic 102(3), 183–198 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  12. Fagin, R., Halpern, J., Moses, Y., Vardi, M.: Reasoning About Knowledge. The MNT Press, Cambridge (1995)

    MATH  Google Scholar 

  13. Kifer, M., Lozinski, L.: A Logic for Reasoning with Inconsistency. J. Automated Deduction 9, 171–215 (1992)

    MathSciNet  Google Scholar 

  14. Kraus, S., Lehmann, D.L.: Knowledge, Belief, and Time. Theoretical Computer Science 98, 143–174 (1988)

    MathSciNet  MATH  Google Scholar 

  15. Moses, Y., Shoham, Y.: Belief and Defeasible Knowledge. Artificial Intelligence 64(2), 299–322 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  16. Nebel, B.: Reasoning and Revision in Hybrid Representation Systems. LNCS, vol. 422. Springer, Heidelberg (1990)

    MATH  Google Scholar 

  17. Neiger, G., Tuttle, M.R.: Common knowledge and consistent simultaneous coordination. Distributed Computing 5(3), 334–352 (1993)

    MATH  Google Scholar 

  18. Nguyen, N.T., et al. (eds.): KES-AMSTA 2008. LNCS (LNAI), vol. 4953. Springer, Heidelberg (2008)

    Google Scholar 

  19. Nguyen, N.T., Huang, D.S.: Knowledge Management for Autonomous Systems and Computational Intelligence. Journal of Universal Computer Science 15(4) (2008)

    Google Scholar 

  20. Nguyen, N.T., Katarzyniak, R.: Actions and Social Interactions in Multi-agent Systems. Special issue for International Journal of Knowledge and Information Systems 18(2) (2009)

    Google Scholar 

  21. Quantz, J., Schmitz, B.: Knowledge-based disambiguation of machine translation. Minds and Machines 9, 97–99 (1996)

    Google Scholar 

  22. Rybakov, V.V.: Admissible Logical Inference Rules. Studies in Logic and the Foundations of Mathematics, vol. 136. Elsevier Sci. Publ., North-Holland, New-York, Amsterdam (1997)

    MATH  Google Scholar 

  23. Rybakov, V.V.: Logics of Schemes and Admissible Rules for First-Order Theories. Stud. Fuzziness. Soft. Comp. 24, 566–879 (1999)

    MathSciNet  MATH  Google Scholar 

  24. Rybakov, V.V.: Unification in Common Knowledge Logics. Bulletin of the Section Logic 3(4), 207–215 (2002)

    MathSciNet  MATH  Google Scholar 

  25. Babenyshev, S., Rybakov, V.: Describing Evolutions of Multi-Agent Systems. In: Velásquez, J.D., Ríos, S.A., Howlett, R.J., Jain, L.C. (eds.) KES 2009. LNCS, vol. 5711, pp. 38–45. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  26. Rybakov, V.: Linear Temporal Logic LTK K extended by Multi-Agent Logic K n with Interacting Agents. J. Log. Comput. 19(6), 989–1017 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  27. Rybakov, V.: Algorithm for Decision Procedure in Temporal Logic Treating Uncertainty, Plausibility, Knowledge and Interacting Agents. IJIIT 6(1), 31–45 (2010)

    Google Scholar 

  28. Rybakov, V.: Interpretation of Chance Discovery in Temporal Logic, Admissible Inference Rules. In: Setchi, R., Jordanov, I., Howlett, R.J., Jain, L.C. (eds.) KES 2010. LNCS, vol. 6278, pp. 323–330. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  29. Rychtyckyi, N.: DLMS: An evaluation of KL-ONE in the automobile industry. In: Aiello, L.C., Doyle, J., Shapiro, S. (eds.) Proc. of he 5-th Int. Conf. on Principles of Knowledge Representation and Reasoning (KR 1996), Cambridge, Mass, pp. 588–596. Morgan Kaufmann, San Francisco (1996)

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Computing, Mathematics and IT, Manchester Metropolitan University, Manchester, M1 5GD, UK

    Vladimir V. Rybakov

  2. Institutes of Mathematics, Siberian Federal University, Krasonoyarsk, Russia

    Vladimir V. Rybakov

Authors
  1. Vladimir V. Rybakov
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Editors and Affiliations

  1. Institute of Integrated Sensor Systems, University of Kaiserslautern, Erwin-Schroedinger-str. 12, 67663, Kaiserslautern, Germany

    Andreas König

  2. Knowledge-Based Systems Group, Department of omputer Science, University of Kaiserslautern, P.O. Box 3049, 67653, Kaiserslautern, Germany

    Andreas Dengel

  3. School of Business, University of Applied Sciences Northwestern Switzerland, Riggenbachstr. 16, 4600, Olten, Switzerland

    Knut Hinkelmann

  4. Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, 599-8531, Sakai, Osaka, Japan

    Koichi Kise

  5. KES International, P.O. Box 2115, BN43 9AF, Shoreham-by-sea, UK

    Robert J. Howlett

  6. University of South Australia, Mawson Lakes, 5095, Adelaide, SA, Australia

    Lakhmi C. Jain

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© 2011 Springer-Verlag Berlin Heidelberg

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Rybakov, V.V. (2011). Agents’ Logics with Common Knowledge and Uncertainty: Unification Problem, Algorithm for Construction Solutions. In: König, A., Dengel, A., Hinkelmann, K., Kise, K., Howlett, R.J., Jain, L.C. (eds) Knowledge-Based and Intelligent Information and Engineering Systems. KES 2011. Lecture Notes in Computer Science(), vol 6881. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23851-2_18

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  • DOI: https://doi.org/10.1007/978-3-642-23851-2_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23850-5

  • Online ISBN: 978-3-642-23851-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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