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International Workshop on Conditionals, Information, and Inference

WCII 2002: Conditionals, Information, and Inference pp 108–130Cite as

Assertions, Conditionals, and Defaults

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3301))

Abstract

A logical framework that emphasizes the impact of affirmative assertions is investigated with respect to providing an interpretation for conditionals and defaults. We consider theories consisting essentially of monadic subsumption statements.For every such theory there is an associated domain of information states ordered by a specialization relation. We show how to naturally interpret intuitionistic conditionals in this information domain. Moreover, we study several ways to cope with defaults. In particular, we adapt the approaches of Poole and Reiter to our framework.

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References

  1. Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. In: Cambridge Tracts in Theoretical Computer Science, vol. 53. Cambridge University Press, Cambridge (2001)

    Google Scholar 

  2. Brewka, G., Eiter, T.: Prioritizing default logic. In: Hölldobler, S. (ed.) Intellectics and Computational Logic. Applied Logic Series, vol. 19, Kluwer, Dordrecht (2000)

    Chapter  MATH  Google Scholar 

  3. Clarke, M.R.B.: Intuitionistic non-monotonic reasoning – further results. In: Proceedings of the 8th European Conference on Artificial Intelligence (ECAI 1988), pp. 525–527 (1988)

    Google Scholar 

  4. Coquand, T., Zhang, G.-Q.: Sequents, Frames, and Completeness. In: Clote, P.G., Schwichtenberg, H. (eds.) CSL 2000. LNCS, vol. 1862, pp. 277–291. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  5. Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order, 2nd edn. Cambridge University Press, Cambridge (2002)

    Book  MATH  Google Scholar 

  6. Droste, M., Göbel, R.: Non-deterministic information systems and their domains. Theoretical Computer Science 75, 289–309 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  7. Gabbay, D.M.: Intuitionistic basis for non-monotonic logic. In: Loveland, D.W. (ed.) CADE 1982. LNCS, vol. 138, pp. 260–273. Springer, Heidelberg (1982)

    Chapter  Google Scholar 

  8. Horn, L.R.: A Natural History of Negation. University of Chicago Press, Chicago (1989)

    Google Scholar 

  9. Lifschitz, V.: Foundations of logic programming. In: Brewka, G. (ed.) Principles of Knowledge Representation. Studies in Logic, Language, and Computation, pp. 69–127. CSLI Publications, Stanford (1996)

    MATH  Google Scholar 

  10. Makinson, D.: General patterns in nonmonotonic reasoning. In: Gabbay, D.M., Hogger, C.J., Robinson, J.A. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming. Nonmonotonic Reasoning and Uncertain Reasoning, vol. 3, pp. 35–110. Oxford University Press, Oxford (1994)

    Google Scholar 

  11. Marek, V.W., Truszczynski, M.: Nonmonotonic Logic. Springer, Berlin (1993)

    Book  MATH  Google Scholar 

  12. McDermott, D.: Nonmonotonic logic. II. Nonmonotonic modal theories. Journal of the Association for Computing Machinery 29(1), 33–57 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  13. McDermott, D., Doyle, J.: Nonmonotonic logic. I. Artificial Intelligence 13(1-2), 41–72 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  14. Oles, F.J.: An application of lattice theory to knowledge representation. Theoretical Computer Science 249, 163–196 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  15. Osswald, R.: A Logic of Classification – with Applications to Linguistic Theory. PhD thesis, FernUniversität Hagen, Fachbereich Informatik (2002), http://pi7.fernuni-hagen.de/osswald/papers/osswald-phd.pdf

  16. Poole, D.: A logical framework for default reasoning. Artificial Intelligence 36, 27–47 (1988)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  18. Rounds, W.C., Zhang, G.-Q.: Domain theory meets default logic. Journal of Logic and Computation 5(1), 1–25 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  19. Rounds, W.C., Zhang, G.-Q.: Clausal Logic and Logic Programming in Algebraic Domains. Information and Computation 171(2), 183–200 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  20. Shoham, Y.: Reasoning about Change. MIT Press, Cambridge (1988)

    MATH  Google Scholar 

  21. Smyth, M.B.: Power domains and predicate transformers: A topological view. In: Díaz, J. (ed.) ICALP 1983. LNCS, vol. 154, pp. 662–675. Springer, Heidelberg (1983)

    Chapter  Google Scholar 

  22. van Dalen, D.: Intuitionistic logic. In: Gabbay, D.M., Guenthner, F. (eds.) Handbook of Philosophical Logic, Alternatives to Classical Logic, vol. III, pp. 225–339. D. Reidel, Dordrecht (1986)

    Chapter  MATH  Google Scholar 

  23. Vickers, S.: Topology via Logic. In: Cambridge Tracts in Theoretical Computer Science, vol. 5. Cambridge University Press, Cambridge (1989)

    Google Scholar 

  24. Zhang, G.-Q., Rounds, W.C.: Defaults in domain theory. Theoretical Computer Science 177(1), 155–182 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  25. Zhang, G.-Q., Rounds, W.C.: Power defaults. In: Fuhrbach, U., Dix, J., Nerode, A. (eds.) LPNMR 1997. LNCS, vol. 1265, pp. 152–169. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Praktische Informatik VII, FernUniversität in Hagen, Universitätsstraße 1, 58084, Hagen, Germany

    Rainer Osswald

Authors
  1. Rainer Osswald
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Editor information

Editors and Affiliations

  1. Dept. of Computer Science, TU Dortmund, 44221, Dortmund, Germany

    Gabriele Kern-Isberner

  2. FernUniversität in Hagen, Fachbereich Wirtschaftswissenschaft, Lehrstuhl für BWL, insb. Operations Research, 58084, Hagen, Germany

    Wilhelm Rödder

  3. FernUniversität in Hagen, Fachbereich Wirtschaftswissenschaft, Lehrstuhl BWL, insb. Operations Research, 58084, Hagen, Germany

    Friedhelm Kulmann

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© 2005 Springer-Verlag Berlin Heidelberg

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Osswald, R. (2005). Assertions, Conditionals, and Defaults. In: Kern-Isberner, G., Rödder, W., Kulmann, F. (eds) Conditionals, Information, and Inference. WCII 2002. Lecture Notes in Computer Science(), vol 3301. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11408017_7

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  • DOI: https://doi.org/10.1007/11408017_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25332-7

  • Online ISBN: 978-3-540-32235-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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