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Reasoning Using Knots

  • Conference paper
Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5330))

Abstract

The deployment of Description Logics (DLs) and Answer Set Programming (ASP), which are well-known knowledge representation and reasoning formalisms, to a growing range of applications has created the need for novel reasoning algorithms and methods. Recently, knots have been introduced as a tool to facilitate reasoning tasks in extensions of ASP with functions symbols. They were then also fruitfully applied for query answering in Description Logics, hinging on the forest-shaped model property of knowledge bases. This paper briefly reviews the knot idea at a generic level and recalls some of the results obtained with them. It also discusses features of knots and relations to other reasoning techniques, and presents issues for further research.

This work has been partially supported by the Austrian Science Fund (FWF) grants P20840 and P20841, and the Mexican National Council for Science and Technology (CONACYT) grant 187697.

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References

  1. Andréka, H., Németi, I., van Benthem, J.: Modal languages and bounded fragments of predicate logic. Journal of Philosophical Logic 27(3), 217–274 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  2. Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P.F. (eds.): The Description Logic Handbook: Theory, Implementation and Applications. Cambridge University Press, Cambridge (2003)

    MATH  Google Scholar 

  3. Baader, F., Sattler, U.: An overview of tableau algorithms for description logics. Studia Logica 69(1), 5–40 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. Baral, C.: Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press, Cambridge (2003)

    Book  MATH  Google Scholar 

  5. Baselice, S., Bonatti, P.A., Criscuolo, G.: On finitely recursive programs. In: Dahl, V., Niemelä, I. (eds.) ICLP 2007. LNCS, vol. 4670, pp. 89–103. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  6. Bonatti, P., Baselice, S.: Composing normal programs with function symbols. In: Proc. of ICLP 2008. LNCS. Springer, Heidelberg (to appear, 2008)

    Google Scholar 

  7. Calimeri, F., Cozza, S., Ianni, G., Leone, N.: Computable functions in ASP: Theory and implementation. In: Proc. of ICLP 2008. LNCS, vol. 5366, Springer, Heidelberg (2008)

    Google Scholar 

  8. Calvanese, D., De Giacomo, G., Lenzerini, M.: Reasoning in expressive description logics with fixpoints based on automata on infinite trees. In: Proc. of the 16th Int. Joint Conf. on Artificial Intelligence (IJCAI 1999), pp. 84–89 (1999)

    Google Scholar 

  9. Calvanese, D., Eiter, T., Ortiz, M.: Answering regular path queries in expressive description logics: An automata-theoretic approach. In: Proc. of the 22nd Nat. Conf. on Artificial Intelligence (AAAI 2007), pp. 391–396 (2007)

    Google Scholar 

  10. de Bruijn, J., Eiter, T., Polleres, A., Tompits, H.: On representational issues about combinations of classical theories with nonmonotonic rules. In: Lang, J., Lin, F., Wang, J. (eds.) KSEM 2006. LNCS, vol. 4092, pp. 1–22. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  11. Eiter, T., Faber, W., Leone, N., Pfeifer, G., Polleres, A.: A logic programming approach to knowledge-state planning: Semantics and complexity. ACM Trans. Comput. Log. 5(2), 206–263 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  12. Eiter, T., Gottlob, G., Ortiz, M., Šimkus, M.: Query answering in the description logic Horn-\(\mathcal{SHIQ}\). In: Proc. of JELIA 2008. LNCS. Springer, Heidelberg (to appear, 2008)

    Google Scholar 

  13. Eiter, T., Lutz, C., Ortiz, M., Šimkus, M.: Complexity of Conjunctive Query Answering in Description Logics with Transitive Roles. Technical report (preliminary), INFSYS RR-1843-08-09, TU Wien (2008)

    Google Scholar 

  14. Fox, D., Gomes, C.P. (eds.): Proceedings of the Twenty-Third AAAI Conference on Artificial Intelligence, AAAI 2008, Chicago, Illinois, USA, July 13-17. AAAI Press, Menlo Park (2008)

    Google Scholar 

  15. Gelfond, M., Lifschitz, V.: Classical Negation in Logic Programs and Disjunctive Databases. New Generation Computing 9, 365–385 (1991)

    Article  MATH  Google Scholar 

  16. Glimm, B., Horrocks, I., Lutz, C., Sattler, U.: Conjunctive query answering for the description logic \(\mathcal{SHIQ}\). In: Proc. of IJCAI 2007, pp. 399–404 (2007)

    Google Scholar 

  17. Glimm, B., Horrocks, I., Sattler, U.: Conjunctive query entailment for \(\mathcal{SHOQ}\). In: Proc. of the 2007 Description Logic Workshop (DL 2007). CEUR Electronic Workshop Proceedings, vol. 250, pp. 65–75 (2007), http://ceur-ws.org/Vol-250/

  18. Grädel, E., Kolaitis, P.G., Vardi, M.Y.: On the decision problem for two-variable first-order logic. Bulletin of Symbolic Logic 3(1), 53–69 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  19. Hustadt, U., Motik, B., Sattler, U.: A decomposition rule for decision procedures by resolution-based calculi. In: Baader, F., Voronkov, A. (eds.) LPAR 2004. LNCS, vol. 3452, pp. 21–35. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  20. Marek, V.W., Remmel, J.B.: On the expressibility of stable logic programming. Theory and Practice of Logic Programming 3, 551–567 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  21. Marek, W., Nerode, A., Remmel, J.: How Complicated is the Set of Stable Models of a Recursive Logic Program? Annals of Pure and Applied Logic 56, 119–135 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  22. Marek, W., Nerode, A., Remmel, J.: The Stable Models of a Predicate Logic Program. Journal of Logic Programming 21(3), 129–153 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  23. Marek, W., Truszczyński, M.: Nonmonotonic Logics – Context-Dependent Reasoning. Springer, Heidelberg (1993)

    MATH  Google Scholar 

  24. Motik, B., Horrocks, I., Rosati, R., Sattler, U.: Can OWL and logic programming live together happily ever after? In: Cruz, I., Decker, S., Allemang, D., Preist, C., Schwabe, D., Mika, P., Uschold, M., Aroyo, L.M. (eds.) ISWC 2006. LNCS, vol. 4273, pp. 501–514. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  25. Németi, I.: Free algebras and decidability in algebraic logic. DSc. thesis, Mathematical Institute of The Hungarian Academy of Sciences, Budapest (1986)

    Google Scholar 

  26. Ortiz, M., Calvanese, D., Eiter, T.: Data complexity of query answering in expressive description logics via tableaux. J. of Automated Reasoning (June 2008)

    Google Scholar 

  27. Ortiz, M., Šimkus, M., Eiter, T.: Conjunctive query answering in \(\mathcal{SH}\) using knots. In: Baader, F., Lutz, C., Motik, B. (eds.) Proc. of DL 2008, Dresden, Germany, May 13-16. CEUR Workshop Proceedings, vol. 353 (2008), CEUR-WS.org

  28. Ortiz, M., Šimkus, M., Eiter, T.: Worst-case optimal conjunctive query answering for an expressive description logic without inverses. In: Fox and Gomes [14], pp. 504–510

    Google Scholar 

  29. Pratt, V.R.: Models of program logics. In: FOCS, pp. 115–122. IEEE, Los Alamitos (1979)

    Google Scholar 

  30. Pratt-Hartmann, I.: Complexity of the guarded two-variable fragment with counting quantifiers. J. Log. Comput. 17(1), 133–155 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  31. Rosati, R.: Integrating Ontologies and Rules: Semantic and Computational Issues. In: Barahona, P., Bry, F., Franconi, E., Henze, N., Sattler, U. (eds.) Reasoning Web 2006. LNCS, vol. 4126, pp. 128–151. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  32. Rudolph, S., Krötzsch, M., Hitzler, P.: Terminological reasoning in \(\mathcal{SHIQ}\) with ordered binary decision diagrams. In: Fox and Gomes [14], pp. 529–534

    Google Scholar 

  33. Šimkus, M., Eiter, T.: FDNC: Decidable non-monotonic disjunctive logic programs with function symbols. In: Proceedings of LPAR 2007. LNCS, vol. 4790, pp. 514–530. Springer, Heidelberg (2007); Full paper Tech. Rep. INFSYS RR-1843-08-01, TU Vienna, http://www.kr.tuwien.ac.at/research/reports/rr0801.pdf

    Google Scholar 

  34. Vardi, M.Y., Wolper, P.: Automata-theoretic techniques for modal logics of programs. J. Comput. Syst. Sci. 32, 183–221 (1986)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Information Systems, Vienna University of Technology, Austria

    Thomas Eiter, Magdalena Ortiz & Mantas Šimkus

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  1. Thomas Eiter
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  2. Magdalena Ortiz
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  3. Mantas Šimkus
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Editor information

Editors and Affiliations

  1. Carnegie Mellon University, Doha, Qatar

    Iliano Cervesato

  2. Technische Universität Darmstadt, Germany

    Helmut Veith

  3. University of Manchester, UK

    Andrei Voronkov

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Eiter, T., Ortiz, M., Šimkus, M. (2008). Reasoning Using Knots. In: Cervesato, I., Veith, H., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2008. Lecture Notes in Computer Science(), vol 5330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89439-1_27

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  • DOI: https://doi.org/10.1007/978-3-540-89439-1_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89438-4

  • Online ISBN: 978-3-540-89439-1

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