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Polynomially Bounded Forgetting

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PRICAI 2014: Trends in Artificial Intelligence (PRICAI 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8862))

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Abstract

Forgetting is one of the most important concepts in logic based problem solving, both from a theoretical and a practical point of view. However, the size of the forgetting result is exponential in worst case. To address this issue, we consider the problem of polynomially bounded forgetting, i.e., when the size of the forgetting result can be expressed polynomially. We coin the notion of polynomially bounded forgetting and distinguish several different levels. We then show that forgetting a set of variables under a polynomial bound can be reduced to forgetting a single one. However, checking variable polynomially bounded forgetting is \(\Sigma_2^P\) complete. Hence, we identify some sufficient conditions for this problem. Finally, we consider polynomially bounded forgetting in CNF formulas.

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References

  1. Buchfuhrer, D., Umans, C.: The complexity of boolean formula minimization. J. Comput. Syst. Sci. 77(1), 142–153 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  2. Cadoli, M., Donini, F.M., Liberatore, P., Schaerf, M.: Space efficiency of propositional knowledge representation formalisms. J. Artif. Intell. Res. (JAIR) 13, 1–31 (2000)

    Google Scholar 

  3. Coste-Marquis, S., Lang, J., Liberatore, P., Marquis, P.: Expressive power and succinctness of propositional languages for preference representation. In: KR, pp. 203–212 (2004)

    Google Scholar 

  4. Darwiche, A.: Decomposable negation normal form. J. ACM 48(4), 608–647 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  5. Darwiche, A., Marquis, P.: A knowledge compilation map. J. Artif. Intell. Res. (JAIR) 17, 229–264 (2002)

    Google Scholar 

  6. Dunne, P.E.: On constructing minimal formulae. Comput. J. 54(7), 1067–1075 (2011)

    Article  Google Scholar 

  7. Eén, N., Biere, A.: Effective preprocessing in SAT through variable and clause elimination. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 61–75. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  8. Eiter, T., Wang, K.: Semantic forgetting in answer set programming. Artif. Intell. 172(14), 1644–1672 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  9. Ghilardi, S., Lutz, C., Wolter, F., Zakharyaschev, M.: Conservative extensions in modal logic. In: Advances in Modal Logic, pp. 187–207 (2006)

    Google Scholar 

  10. Herzig, A., Mengin, J.: Uniform interpolation by resolution in modal logic. In: Hölldobler, S., Lutz, C., Wansing, H. (eds.) JELIA 2008. LNCS (LNAI), vol. 5293, pp. 219–231. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  11. Konev, B., Walther, D., Wolter, F.: Forgetting and uniform interpolation in large-scale description logic terminologies. In: IJCAI, pp. 830–835 (2009)

    Google Scholar 

  12. Kontchakov, R., Wolter, F., Zakharyaschev, M.: Can you tell the difference between dl-lite ontologies? In: KR, pp. 285–295 (2008)

    Google Scholar 

  13. Lang, J., Liberatore, P., Marquis, P.: Propositional independence: Formula-variable independence and forgetting. J. Artif. Intell. Res. (JAIR) 18, 391–443 (2003)

    Google Scholar 

  14. Lang, J., Marquis, P.: Resolving inconsistencies by variable forgetting. In: KR, pp. 239–250 (2002)

    Google Scholar 

  15. Lin, F.: On strongest necessary and weakest sufficient conditions. Artif. Intell. 128(1-2), 143–159 (2001)

    Article  MATH  Google Scholar 

  16. Lin, F., Reiter, R.: Forget it! In: Proceedings of the AAAI Fall Symposium on Relevance, pp. 154–159 (1994)

    Google Scholar 

  17. Lin, F., Reiter, R.: How to progress a database. Artif. Intell. 92(1-2), 131–167 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  18. Lutz, C., Walther, D., Wolter, F.: Conservative extensions in expressive description logics. In: IJCAI, pp. 453–458 (2007)

    Google Scholar 

  19. van Ditmarsch, H., Herzig, A., Lang, J., Marquis, P.: Introspective forgetting. In: Wobcke, W., Zhang, M. (eds.) AI 2008. LNCS (LNAI), vol. 5360, pp. 18–29. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  20. Wang, K., Wang, Z., Topor, R., Pan, J.Z., Antoniou, G.: Concept and role forgetting in \({\mathcal{ALC}}\) ontologies. In: Bernstein, A., Karger, D.R., Heath, T., Feigenbaum, L., Maynard, D., Motta, E., Thirunarayan, K. (eds.) ISWC 2009. LNCS, vol. 5823, pp. 666–681. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  21. Wang, Y., Zhang, Y., Zhou, Y., Zhang, M.: Forgetting in logic programs under strong equivalence. In: KR (2012)

    Google Scholar 

  22. Wernhard, C.: Literal projection for first-order logic. In: Hölldobler, S., Lutz, C., Wansing, H. (eds.) JELIA 2008. LNCS (LNAI), vol. 5293, pp. 389–402. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  23. Zhang, Y., Foo, N.Y.: Solving logic program conflict through strong and weak forgettings. Artif. Intell. 170(8-9), 739–778 (2006)

    Article  MathSciNet  Google Scholar 

  24. Zhang, Y., Zhou, Y.: Knowledge forgetting: Properties and applications. Artif. Intell. 173(16-17), 1525–1537 (2009)

    Article  MATH  Google Scholar 

  25. Zhang, Y., Zhou, Y.: Forgetting revisited. In: KR (2010)

    Google Scholar 

  26. Zhou, Y., Zhang, Y.: Bounded forgetting. In: AAAI (2011)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Artificial Intelligence Research Group, School of Computing, Engineering and Mathematics, University of Western Sydney, Australia

    Yi Zhou

Authors
  1. Yi Zhou
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Editor information

Editors and Affiliations

  1. MIMOS Berhad Technology Park Malaysia, 57000, Bukit Jalil, KL, Malaysia

    Duc-Nghia Pham

  2. Kyungpook National University, Sankyuk-Dong, Buk-Gu, 702-701, Daegu, Korea

    Seong-Bae Park

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Zhou, Y. (2014). Polynomially Bounded Forgetting. In: Pham, DN., Park, SB. (eds) PRICAI 2014: Trends in Artificial Intelligence. PRICAI 2014. Lecture Notes in Computer Science(), vol 8862. Springer, Cham. https://doi.org/10.1007/978-3-319-13560-1_34

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  • DOI: https://doi.org/10.1007/978-3-319-13560-1_34

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13559-5

  • Online ISBN: 978-3-319-13560-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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