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Default Reasoning over Domains and Concept Hierarchies

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KI 2004: Advances in Artificial Intelligence (KI 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3238))

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Abstract

W.C. Rounds and G.-Q. Zhang have proposed to study a form of disjunctive logic programming generalized to algebraic domains [1]. This system allows reasoning with information which is hierarchically structured and forms a (suitable) domain. We extend this framework to include reasoning with default negation, giving rise to a new nonmonotonic reasoning framework on hierarchical knowledge which encompasses answer set programming with extended disjunctive logic programs. We also show that the hierarchically structured knowledge on which programming in this paradigm can be done, arises very naturally from formal concept analysis. Together, we obtain a default reasoning paradigm for conceptual knowledge which is in accordance with mainstream developments in nonmonotonic reasoning.

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References

  1. Rounds, W.C., Zhang, G.Q.: Clausal logic and logic programming in algebraic domains. Information and Computation 171, 156–182 (2001)

    Article  MathSciNet  Google Scholar 

  2. Abramsky, S., Jung, A.: Domain theory. In: Abramsky, S., Gabbay, D., Maibaum, T.S. (eds.) Handbook of Logic in Computer Science, Clarendon, Oxford, vol. 3 (1994)

    Google Scholar 

  3. Reiter, R.: A logic for default reasoning. Artificial Intelligence 13, 81–132 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  4. Eiter, T., Leone, N., Mateis, C., Pfeifer, G., Scarcello, F.: A deductive system for nonmonotonic reasoning. In: Fuhrbach, U., Dix, J., Nerode, A. (eds.) LPNMR 1997. LNCS, vol. 1265, Springer, Heidelberg (1997)

    Google Scholar 

  5. Simons, P., Niemelä, I., Soininen, T.: Extending and implementing the stable model semantics. Artificial Intelligence (200x) (to appear)

    Google Scholar 

  6. Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 365–385 (1991)

    Article  Google Scholar 

  7. Hitzler, P., Wendt, M.: Formal concept analysis and resolution in algebraic domains. In: de Moor, A., Ganter, B. (eds.) Using Conceptual Structures – Contributions to ICCS 2003, pp. 157–170. Shaker Verlag, Aachen (2003)

    Google Scholar 

  8. Ganter, B., Wille, R.: Formal Concept Analysis – Mathematical Foundations. Springer, Berlin (1999)

    MATH  Google Scholar 

  9. Scott, D.S.: Domains for denotational semantics. In: Nielsen, M., Schmidt, E.M. (eds.) ICALP 1982. LNCS, vol. 140, pp. 577–613. Springer, Heidelberg (1982)

    Chapter  Google Scholar 

  10. Hofmann, K.H., Mislove, M.W.: Local compactness and continuous lattices. In: Lee, J.P., Grinstein, G.G. (eds.) Visualization-WS 1993. LNCS, vol. 871, pp. 209–248. Springer, Heidelberg (1994)

    Google Scholar 

  11. Plotkin, G.: Tω as a universal domain. Journal of Computer and System Sciences 17, 209–236 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  12. Fitting, M.: A Kripke-Kleene-semantics for general logic programs. The Journal of Logic Programming 2, 295–312 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  13. Hitzler, P.: A resolution theorem for algebraic domains. In: Gottlob, G., Walsh, T. (eds.) Proceedings of the 18th International Joint Conference on Artificial Intelligence, Acapulco, Mexico, August 2003, pp. 1339–1340. Morgan Kaufmann Publishers, San Francisco (2003)

    Google Scholar 

  14. Hitzler, P.: A generalized resolution theorem. Journal of Electrial Engineering, Slovak Academy of Sciences 55, 25–30 (2003)

    Google Scholar 

  15. Makinson, D.: Bridges between classical and nonmonotonic logic. Logic Journal of the IGPL 11, 69–96 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  16. Lloyd, J.W.: Foundations of Logic Programming. Springer, Berlin (1988)

    Google Scholar 

  17. Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Kowalski, R.A., Bowen, K.A. (eds.) Logic Programming. Proceedings of the 5th International Conference and Symposium on Logic Programming, pp. 1070–1080. MIT Press, Cambridge (1988)

    Google Scholar 

  18. Wille, R.: Restructuring lattice theory: An approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets, pp. 445–470. Reidel, Dordrecht (1982)

    Google Scholar 

  19. Ganter, B., Wille, R.: Contextual attribute logic. In: Tepfenhart, W.M. (ed.) ICCS 1999. LNCS, vol. 1640, pp. 377–388. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  20. Wille, R.: Boolean judgement logic. In: Delugach, H.S., Stumme, G. (eds.) ICCS 2001. LNCS (LNAI), vol. 2120, pp. 115–128. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  21. Zhang, G.Q.: Chu spaces, concept lattices, and domains. In: Proceedings of the Nineteenth Conference on the Mathematical Foundations of Programming Semantics, Montreal, Canada, March 2003. Electronic Notes in Theoretical Computer Science, vol. 83 (2003)

    Google Scholar 

  22. Zhang, G.Q., Shen, G.: Approximable concepts, Chu spaces, and information systems. Theory and Applications of Categories (200x) (to appear)

    Google Scholar 

  23. Hitzler, P., Zhang, G.Q.: A cartesian closed category of approximable concept structures. In: Pfeiffer, H., Wolff, K. (eds.) Proceedings of the International Conference On Conceptual Structures, Huntsville, Alabama, USA. LNCS, Springer, Heidelberg (2004) (to appear)

    Google Scholar 

  24. Osswald, R.: Assertions, conditionals, and defaults. In: Kern-Isberner, G., Rödder, W., Kulmann, F. (eds.) WCII 2002. LNCS (LNAI), vol. 3301, pp. 108–130. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  25. Osswald, R., Petersen, W.: A logical approach to data driven classification. In: Günter, A., Kruse, R., Neumann, B. (eds.) KI 2003. LNCS (LNAI), vol. 2821, pp. 267–281. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  26. Zhang, G.Q., Rounds, W.C.: Reasoning with power defaults (preliminary report). In: Fuhrbach, U., Dix, J., Nerode, A. (eds.) LPNMR 1997. LNCS, vol. 1265, pp. 152–169. Springer, Heidelberg (1997)

    Google Scholar 

  27. Zhang, G.Q., Rounds, W.C.: Semantics of logic programs and representation of Smyth powerdomains. In: Keimel, K., et al. (eds.) Domains and Processes, pp. 151–179. Kluwer, Dordrecht (2001)

    Google Scholar 

  28. Hitzler, P., Seda, A.K.: Some issues concerning fixed points in computational logic: Quasi-metrics, multivalued mappings and the Knaster-Tarski theorem. In: Proceedings of the 14th Summer Conference on Topology and its Applications: Special Session on Topology in Computer Science, New York. Topology Proceedings, vol. 24, pp. 223–250 (1999)

    Google Scholar 

  29. Hitzler, P., Seda, A.K.: Generalized metrics and uniquely determined logic programs. Theoretical Computer Science 305, 187–219 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  30. Seda, A.K., Hitzler, P.: Topology and iterates in computational logic. In: Proceedings of the 12th Summer Conference on Topology and its Applications: Special Session on Topology in Computer Science, Ontario, August 1997. Topology Proceedings, vol. 22, pp. 427–469 (1997)

    Google Scholar 

  31. Shastri, L.: Default reasoning in semantic networks: A formalization of recognition and inheritance. Artificial Intelligence 39, 283–355 (1989)

    Article  MATH  Google Scholar 

  32. Baader, F., Hollunder, B.: Embedding defaults into terminological representation systems. J. Automated Reasoning 14, 149–180 (1995)

    Article  MathSciNet  Google Scholar 

  33. Donini, F.M., Nardi, D., Rosati, R.: Description logics of minimal knowledge and negation as failure. ACM Trans. Comput. Logic 3, 177–225 (2002)

    Article  MathSciNet  Google Scholar 

  34. Buccafurri, F., Leone, N.: Disjunctive logic programs with inheritance. Theory and Practice of Logic Programming 2, 293–321 (2002)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Dresden University of Technology,  

    Pascal Hitzler

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  1. Pascal Hitzler
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Editor information

Editors and Affiliations

  1. Institute for Artificial Intelligence, Ulm University, Germany

    Susanne Biundo

  2. Fakultät für Ingenieurwissenschaften und Informatik, Universität Ulm, 89069, Ulm, v

    Thom Frühwirth

  3. Institute of Neural Information Processing, University of Ulm, D-89069, Ulm, Germany

    Günther Palm

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Hitzler, P. (2004). Default Reasoning over Domains and Concept Hierarchies. In: Biundo, S., Frühwirth, T., Palm, G. (eds) KI 2004: Advances in Artificial Intelligence. KI 2004. Lecture Notes in Computer Science(), vol 3238. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30221-6_27

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  • DOI: https://doi.org/10.1007/978-3-540-30221-6_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23166-0

  • Online ISBN: 978-3-540-30221-6

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