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Systems and Implementations for Solving Reasoning Problems in Conditional Logics

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Foundations of Information and Knowledge Systems (FoIKS 2016)

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Abstract

Default rules like “If A, then normally B” or probabilistic rules like “If A, then B with probability x” are powerful constructs for knowledge representation. Such rules can be formalized as conditionals, denoted by \((B|A)\) or \((B|A)[x]\), and a conditional knowledge base consists of a set of conditionals. Different semantical models have been proposed for conditional knowledge bases, and the most important reasoning problems are to determine whether a knowledge base is consistent and to determine what a knowledge base entails. We present an overview on systems and implementations our group has been working on for solving reasoning problems in various semantics that have been developed for conditional knowledge bases. These semantics include quantitative, semi-quantitative, and qualitative conditional logics, based on both propositional logic and on first-order logic.

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Notes

  1. 1.

    KReator can be found at http://kreator-ide.sourceforge.net/.

  2. 2.

    https://www.fernuni-hagen.de/wbs/research/log4kr/index.html.

References

  1. Adams, E.W.: The Logic of Conditionals: An Application of Probability to Deductive Logic. Synthese Library. Springer Science+Business Media, Dordrecht (1975)

    Book  MATH  Google Scholar 

  2. Beierle, C., Eichhorn, C., Kern-Isberner, G.: Skeptical inference based on c-representations and its characterization as a constraint satisfaction problem. In: Gyssens, M., Simari, G. (eds.) FoIKS 2016. LNCS, vol. 9161, pp. 65–82. Springer, Switzerland (2016)

    Google Scholar 

  3. Beierle, C., Finthammer, M., Potyka, N., Varghese, J., Kern-Isberner, G.: A case study on the application of probabilistic conditional modelling and reasoning to clinical patient data in neurosurgery. In: van der Gaag, L.C. (ed.) ECSQARU 2013. LNCS, vol. 7958, pp. 49–60. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  4. Beierle, C., Kern-Isberner, G.: Modelling conditional knowledge discovery and belief revision by abstract state machines. In: Börger, E., Gargantini, A., Riccobene, E. (eds.) ASM 2003. LNCS, vol. 2589, pp. 186–203. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  5. Beierle, C., Kern-Isberner, G.: A verified AsmL implementation of belief revision. In: Börger, E., Butler, M., Bowen, J.P., Boca, P. (eds.) ABZ 2008. LNCS, vol. 5238, pp. 98–111. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  6. Beierle, C., Kern-Isberner, G., Koch, N.: A high-level implementation of a system for automated reasoning with default rules (system description). In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 147–153. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  7. Beierle, C., Kern-Isberner, G., Södler, K.: A declarative approach for computing ordinal conditional functions using constraint logic programming. In: Tompits, H., Abreu, S., Oetsch, J., Pührer, J., Seipel, D., Umeda, M., Wolf, A. (eds.) INAP/WLP 2011. LNCS, vol. 7773, pp. 168–185. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  8. Beierle, C., Krämer, A.: Achieving parametric uniformity for knowledge bases in a relational probabilistic conditional logic with maximum entropy semantics. Ann. Math. Artif. Intell. 73(1–2), 5–45 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  9. Beierle, C., Kuche, S., Finthammer, M., Kern-Isberner, G.: A software system for the computation, visualization, and comparison of conditional structures for relational probabilistic knowledge bases. In: Proceeding of the Twenty-Eigth International Florida Artificial Intelligence Research Society Conference (FLAIRS 2015), pp. 558–563. AAAI Press, Menlo Park (2015)

    Google Scholar 

  10. Beierle, C., Finthammer, M., Kern-Isberner, G.: Relational probabilistic conditionals and their instantiations under maximum entropy semantics for first-order knowledge bases. Entropy 17(2), 852–865 (2015)

    Article  Google Scholar 

  11. Benferhat, S., Dubois, D., Prade, H.: Representing default rules in possibilistic logic. In: Proceedings 3th International Conference on Principles of Knowledge Representation and Reasoning KR 1992, pp. 673–684 (1992)

    Google Scholar 

  12. Delgrande, J.: On first-order conditional logics. Artif. Intell. 105, 105–137 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  13. Dubois, D., Prade, H.: Conditional objects as nonmonotonic consequence relations: main results. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Fourth International Conference (KR 1994), pp. 170–177. Morgan Kaufmann Publishers, San Francisco (1994)

    Google Scholar 

  14. Dubois, D., Prade, H.: Possibility Theory and Its Applications: Where Do We Stand? In: Kacprzyk, J., Pedrycz, W. (eds.) Springer Handbook of Computational Intelligence, pp. 31–60. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  15. Falke, T.: Computation of ranking functions for knowledge bases with relational conditionals. M.Sc. Thesis, Dept. of Computer Science, University of Hagen, Germany (2015)

    Google Scholar 

  16. Finthammer, M., Beierle, C.: Using equivalences of worlds for aggregation semantics of relational conditionals. In: Glimm, B., Krüger, A. (eds.) KI 2012. LNCS, vol. 7526, pp. 49–60. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  17. Finthammer, M., Beierle, C.: A two-level approach to maximum entropy model computation for relational probabilistic logic based on weighted conditional impacts. In: Straccia, U., Calì, A. (eds.) SUM 2014. LNCS, vol. 8720, pp. 162–175. Springer, Heidelberg (2014)

    Google Scholar 

  18. Finthammer, M., Beierle, C.: Towards a more efficient computation of weighted conditional impacts for relational probabilistic knowledge bases under maximum entropy semantics. In: Hölldobler, S., Krötzsch, M., Peñaloza, R., Rudolph, S. (eds.) KI 2015. LNCS, vol. 9324, pp. 72–86. Springer, Heidelberg (2015). doi:10.1007/978-3-319-24489-1_6

    Chapter  Google Scholar 

  19. Finthammer, M., Beierle, C., Berger, B., Kern-Isberner, G.: Probabilistic reasoning at optimum entropy with the MEcore system. In: Lane, H.C., Guesgen, H.W. (eds.) Proceedings 22nd International FLAIRS Conference, FLAIRS 2009, pp. 535–540. AAAI Press, Menlo Park (2009)

    Google Scholar 

  20. Finthammer, M., Thimm, M.: An integrated development environment for probabilistic relational reasoning. Logic J. IGPL 20(5), 831–871 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  21. Fisseler, J.: First-order probabilistic conditional logic and maximum entropy. Logic J. IGPL 20(5), 796–830 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  22. Fisseler, J., Kern-Isberner, G., Beierle, C.: Learning uncertain rules with CondorCKD. In: Proceedings 20th International FLAIRS Conference, FLAIRS 2007. AAAI Press, Menlo Park (2007)

    Google Scholar 

  23. Fisseler, J., Kern-Isberner, G., Beierle, C., Koch, A., Müller, C.: Algebraic knowledge discovery using haskell. In: Hanus, M. (ed.) PADL 2007. LNCS, vol. 4354, pp. 80–93. Springer, Heidelberg (2007). http://dx.doi.org/10.1007/978-3-540-69611-7_5

    Chapter  Google Scholar 

  24. Getoor, L., Taskar, B. (eds.): Introduction to Statistical Relational Learning. MIT Press, Cambridge (2007)

    MATH  Google Scholar 

  25. Goldszmidt, M., Pearl, J.: Qualitative probabilities for default reasoning, belief revision, and causal modeling. Artif. Intell. 84(1–2), 57–112 (1996)

    Article  MathSciNet  Google Scholar 

  26. Gurevich, Y., Rossman, B., Schulte, W.: Semantic essence of AsmL. Theoret. Comput. Sci. 343(3), 370–412 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  27. Halpern, J.Y.: Reasoning About Uncertainty. MIT Press, Cambridge (2005)

    MATH  Google Scholar 

  28. Kern-Isberner, G.: Characterizing the principle of minimum cross-entropy within a conditional-logical framework. Artif. Intell. 98, 169–208 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  29. Kern-Isberner, G.: Solving the inverse representation problem. In: Proceedings 14th European Conference on Artificial Intelligence. ECAI 2000, pp. 581–585. IOS Press, Berlin (2000)

    Google Scholar 

  30. Kern-Isberner, G.: Conditionals in Nonmonotonic Reasoning and Belief Revision. LNCS (LNAI), vol. 2087. Springer, Heidelberg (2001)

    MATH  Google Scholar 

  31. Kern-Isberner, G.: A thorough axiomatization of a principle of conditional preservation in belief revision. Annals Math. Artif. Intell. 40(1–2), 127–164 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  32. Kern-Isberner, G., Beierle, C.: A system Z-like approach for first-order default reasoning. In: Eiter, T., Strass, H., Truszczyński, M., Woltran, S. (eds.) Advances in Knowledge Representation. LNCS, vol. 9060, pp. 81–95. Springer, Heidelberg (2015)

    Google Scholar 

  33. Kern-Isberner, G., Beierle, C., Finthammer, M., Thimm, M.: Comparing and evaluating approaches to probabilistic reasoning: theory, implementation, and applications. Trans. Large-Scale Data Knowl.-Centered Syst. 6, 31–75 (2012)

    Google Scholar 

  34. Kern-Isberner, G., Fisseler, J.: Knowledge discovery by reversing inductive knowledge representation. In: Proceedings of the Ninth International Conference on the Principles of Knowledge Representation and Reasoning, KR-2004, pp. 34–44. AAAI Press (2004)

    Google Scholar 

  35. Kern-Isberner, G., Lukasiewicz, T.: Combining probabilistic logic programming with the power of maximum entropy. Artif. Intell. 157(1–2), 139–202 (2004). Special Issue on Nonmonotonic Reasoning

    Article  MathSciNet  MATH  Google Scholar 

  36. Kern-Isberner, G., Thimm, M.: Novel semantical approaches to relational probabilistic conditionals. In: Lin, F., Sattler, U., Truszczynski, M. (eds.) Proceedings Twelfth International Conference on the Principles of Knowledge Representation and Reasoning, KR 2010, pp. 382–391. AAAI Press (2010)

    Google Scholar 

  37. Kern-Isberner, G., Thimm, M.: A ranking semantics for first-order conditionals. In: De Raedt, L., Bessiere, C., Dubois, D., Doherty, P., Frasconi, P., Heintz, F., Lucas, P. (eds.) Proceedings 20th European Conference on Artificial Intelligence, ECAI-2012, pp. 456–461. No. 242 in Frontiers in Artificial Intelligence and Applications. IOS Press (2012)

    Google Scholar 

  38. Lewis, D.: Counterfactuals. Harvard University Press, Cambridge (1973)

    MATH  Google Scholar 

  39. Nute, D.: Topics in Conditional Logic. D. Reidel Publishing Company, Dordrecht (1980)

    Book  MATH  Google Scholar 

  40. Paris, J.: The Uncertain Reasoner’s Companion - A Mathematical Perspective. Cambridge University Press, Cambridge (1994)

    MATH  Google Scholar 

  41. Paris, J., Vencovska, A.: In defence of the maximum entropy inference process. Int. J. Approximate Reasoning 17(1), 77–103 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  42. Pearl, J.: System Z: A natural ordering of defaults with tractable applications to nonmonotonic reasoning. In: Proceeding of the 3rd Conference on Theoretical Aspects of Reasoning About Knowledge (TARK 1990), pp. 121–135. Morgan Kaufmann Publ. Inc., San Francisco (1990)

    Google Scholar 

  43. Potyka, N.: Linear programs for measuring inconsistency in probabilistic logics. In: Proceedings KR 2014, pp. 568–578. AAAI Press (2014)

    Google Scholar 

  44. Potyka, N.: Solving Reasoning Problems for Probabilistic Conditional Logics with Consistent and Inconsistent Information. Ph.D. thesis, Fernuniversität Hagen, Germany (2015)

    Google Scholar 

  45. Potyka, N., Thimm, M.: Consolidation of probabilistic knowledge bases by inconsistency minimization. In: Proceedings ECAI 2014, pp. 729–734. IOS Press (2014)

    Google Scholar 

  46. Potyka, N., Thimm, M.: Probabilistic reasoning with inconsistent beliefs using inconsistency measures. In: Proceeding of the International Joint Conference on Artificial Intelligence 2015 (IJCAI 2015), pp. 3156–3163 (2015)

    Google Scholar 

  47. Rödder, W., Kern-Isberner, G.: Léa sombé und entropie-optimale informationsverarbeitung mit der expertensystem-shell SPIRIT. OR Spektrum 19(3), 41–46 (1997)

    Article  MATH  Google Scholar 

  48. Rödder, W., Reucher, E., Kulmann, F.: Features of the expert-system-shell SPIRIT. Logic J. IGPL 14(3), 483–500 (2006)

    Article  MATH  Google Scholar 

  49. Spohn, W.: Ordinal conditional functions: a dynamic theory of epistemic states. In: Harper, W., Skyrms, B. (eds.) Causation in Decision, Belief Change, and Statistics, II, pp. 105–134. Kluwer Academic Publishers (1988)

    Google Scholar 

  50. Spohn, W.: The Laws of Belief: Ranking Theory and Its Philosophical Applications. Oxford University Press, Oxford (2012)

    Book  Google Scholar 

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Acknowledgments

A large part of the work reported here was done in cooperation and in joint projects with Gabriele Kern-Isberner and her research group at TU Dortmund University, Germany. I am also very grateful to all members of the project teams involved, in particular to Marc Finthammer, Jens Fisseler, Nico Potyka, Matthias Thimm, and numerous students for their contributions.

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  1. Faculty of Mathematics and Computer Science, University of Hagen, 58084, Hagen, Germany

    Christoph Beierle

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  1. Christoph Beierle
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Correspondence to Christoph Beierle .

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  1. Faculteit Wetenschappen, Universiteit Hasselt, Hasselt, Belgium

    Marc Gyssens

  2. Dept. Ciencias Ingeniería Computación, Universidad Nacional del Sur, Bahía Blanca, Argentina

    Guillermo Simari

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Beierle, C. (2016). Systems and Implementations for Solving Reasoning Problems in Conditional Logics. In: Gyssens, M., Simari, G. (eds) Foundations of Information and Knowledge Systems. FoIKS 2016. Lecture Notes in Computer Science(), vol 9616. Springer, Cham. https://doi.org/10.1007/978-3-319-30024-5_5

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  • DOI: https://doi.org/10.1007/978-3-319-30024-5_5

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