Abstract
The handling of uncertain information is of crucial importance for the success of expert systems. This paper gives an overview on logic-based approaches to probabilistic reasoning and goes into more details about recent developments for relational, respectively first-order, probabilistic methods like Markov logic networks, and Bayesian logic programs. In particular, we feature the maximum entropy approach as a powerful and elegant method that combines convenience with respect to knowledge representation with excellent inference properties. While comparing the different approaches is a difficult task due to the variety of the available concepts and to the absence of a common interface, we address this problem from both a conceptual and practical point of view. On a conceptual layer we propose and discuss several criteria by which first-order probabilistic methods can be distinguished, and apply these criteria to a series of approaches. On the practical layer, we briefly describe some systems for probabilistic reasoning, and go into more details on the KReator system as a versatile toolbox for various approaches to first-order probabilistic relational learning, modelling, and reasoning. Moreover, we illustrate applications of probabilistic logics in various scenarios.
Keywords
- Bayesian Network
- Maximum Entropy
- Knowledge Representation
- Inductive Logic Programming
- Conditional Probability Distribution
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The research reported here was partially supported by the Deutsche Forschungsgemeinschaft (grants KE 1413/2-2 and BE 1700/7-2).
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References
Baral, C., Gelfond, M., Rushton, N.: Probabilistic Reasoning with Answer Sets. Theory and Practice of Logic Programming 9, 57–144 (2009)
Baumbach, J., Bunkowski, A., Lange, S., Oberwahrenbrock, T., Kleinbölting, N., Rahmen, S., Baumbach, J.I.: IMS2 – An integrated medical software system for early lung cancer detection using ion mobility spectometry data of human breath. J. of Integrative Bioinformatics 4(3) (2007)
Baumbach, J.I., Westhoff, M.: Ion mobility spectometry to detect lung cancer and airway infections. Spectroscopy Europe 18(6), 22–27 (2006)
Beierle, C., Finthammer, M., Kern-Isberner, G., Thimm, M.: Evaluation and Comparison Criteria for Approaches to Probabilistic Relational Knowledge Representation. In: Bach, J., Edelkamp, S. (eds.) KI 2011. LNCS, vol. 7006, pp. 63–74. Springer, Heidelberg (2011)
Beierle, C., Kern-Isberner, G.: The Relationship of the Logic of Big-Stepped Probabilities to Standard Probabilistic Logics. In: Link, S., Prade, H. (eds.) FoIKS 2010. LNCS, vol. 5956, pp. 191–210. Springer, Heidelberg (2010)
Bödeker, B., Vautz, W., Baumbach, J.I.: Peak finding and referencing in MCC/IMS-data. International Journal for Ion Mobility Spectrometry 11(1-4), 83–87 (2008)
Breese, J.S.: Construction of Belief and Decision Networks. Computational Intelligence 8(4), 624–647 (1992)
Broecheler, M., Simari, G.I., Subrahmanian, V.S.: Using Histograms to Better Answer Queries to Probabilistic Logic Programs. In: Hill, P.M., Warren, D.S. (eds.) ICLP 2009. LNCS, vol. 5649, pp. 40–54. Springer, Heidelberg (2009)
Bruynooghe, M., De Cat, B., Drijkoningen, J., Fierens, D., Goos, J., Gutmann, B., Kimmig, A., Labeeuw, W., Langenaken, S., Landwehr, N., Meert, W., Nuyts, E., Pellegrims, R., Rymenants, R., Segers, S., Thon, I., Van Eyck, J., Van den Broeck, G., Vangansewinkel, T., Van Hove, L., Vennekens, J., Weytjens, T., De Raedt, L.: An Exercise with Statistical Relational Learning Systems. In: Domingos, P., Kersting, K. (eds.) International Workshop on Statistical Relational Learning (SRL 2009), Leuven, Belgium (2009)
Chavira, M., Darwiche, A., Jaeger, M.: Compiling relational Bayesian networks for exact inference. International Journal of Approximate Reasoning 42(1-2), 4–20 (2006)
Cussens, J.: Logic-based formalisms for statistical relational learning. In: Getoor, L., Taskar, B. (eds.) Introduction to Statistical Relational Learning. MIT Press, Cambridge (2007)
Darroch, J.N., Ratcliff, D.: Generalized iterative scaling for log-linear models. In: Annals of Mathematical Statistics, vol. 43, pp. 1470–1480. Institute of Mathematical Statistics (1972)
De Raedt, L., Kersting, K.: Probabilistic Inductive Logic Programming. In: De Raedt, L., Frasconi, P., Kersting, K., Muggleton, S. (eds.) Probabilistic ILP 2007. LNCS (LNAI), vol. 4911, pp. 1–27. Springer, Heidelberg (2008)
Dehaspe, L.: Maximum Entropy Modeling with Clausal Constraints. In: Džeroski, S., Lavrač, N. (eds.) ILP 1997. LNCS, vol. 1297, pp. 109–125. Springer, Heidelberg (1997)
Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum-likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society, Series B 39(1), 1–38 (1977)
Domingos, P., Lowd, D.: Markov Logic: An Interface Layer for Artificial Intelligence. In: Synthesis Lectures on Artificial Intelligence and Machine Learning. Morgan and Claypool, San Rafael (2009)
Fagin, R., Halpern, J.Y.: Reasoning about knowledge and probability. J. ACM 41(2), 340–367 (1994)
Fierens, D.: Learning Directed Probabilistic Logical Models from Relational Data. PhD thesis, Katholieke Universiteit Leuven (2008)
Finthammer, M.: An Iterative Scaling Algorithm for Maximum Entropy Reasoning in Relational Probabilistic Conditional Logic. In: Hüllermeier, E. (ed.) SUM 2012. LNCS (LNAI), vol. 7520, pp. 351–364. Springer, Heidelberg (2012)
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. AAAI Press, Menlo Park (2009)
Finthammer, M., Beierle, C., Fisseler, J., Kern-Isberner, G., Baumbach, J.I.: Using probabilistic relational learning to support bronchial carcinoma diagnosis based on ion mobility spectrometry. International Journal for Ion Mobility Spectrometry 13, 83–93 (2010)
Finthammer, M., Thimm, M.: An Integrated Development Environment for Probabilistic Relational Reasoning. International Journal of the IGPL (2011) (to appear)
Fisseler, J.: Toward Markov Logic with Conditional Probabilities. In: Wilson, D.C., Lane, H.C. (eds.) Proceedings of the 21st International FLAIRS Conference, FLAIRS 2008, pp. 643–648. AAAI Press (2008)
Fisseler, J.: Learning and Modeling with Probabilistic Conditional Logic. Dissertations in Artificial Intelligence, vol. 328. IOS Press, Amsterdam (2010)
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)
Gamma, E., Helm, R., Johnson, R., Vlissides, J.: Design Patterns: Elements of Reusable Object-Oriented Software. Addison-Wesley (1994)
Getoor, L., Friedman, N., Koller, D., Tasker, B.: Learning Probabilistic Models of Relational Structure. In: Brodley, C.E., Danyluk, A.P. (eds.) Proceedings of the 18th International Conference on Machine Learning, ICML 2001, pp. 170–177. Morgan Kaufmann (2001)
Getoor, L., Grant, J.: PRL: A probabilistic relational language. Machine Learning 62(1), 7–31 (2006)
Getoor, L., Taskar, B. (eds.): Introduction to Statistical Relational Learning. MIT Press (2007)
Gosling, J., Joy, B., Steele, G., Bracha, G.: The Java Language Specification, 3rd edn. Addison-Wesley (2005)
Jaeger, M.: Relational Bayesian Networks: A Survey. Electronic Transactions in Artificial Intelligence 6 (2002)
Jaeger, M.: Model-Theoretic Expressivity Analysis. In: De Raedt, L., Frasconi, P., Kersting, K., Muggleton, S. (eds.) Probabilistic ILP 2007. LNCS (LNAI), vol. 4911, pp. 325–339. Springer, Heidelberg (2008)
Jain, D., Mösenlechner, L., Beetz, M.: Equipping Robot Control Programs with First-Order Probabilistic Reasoning Capabilities. In: International Conference on Robotics and Automation (ICRA), pp. 3130–3135 (2009)
Jensen, F.V., Nielsen, T.D.: Bayesian Networks and Decision Graphs. Springer (2007)
Kern-Isberner, G.: Characterizing the principle of minimum cross-entropy within a conditional-logical framework. Artificial Intelligence 98, 169–208 (1998)
Kern-Isberner, G.: Conditionals in Nonmonotonic Reasoning and Belief Revision. LNCS (LNAI), vol. 2087. Springer, Heidelberg (2001)
Kern-Isberner, G.: Linking iterated belief change operations to nonmonotonic reasoning. In: Brewka, G., Lang, J. (eds.) Proceedings 11th International Conference on Knowledge Representation and Reasoning, KR 2008, pp. 166–176. AAAI Press, Menlo Park (2008)
Kern-Isberner, G., Beierle, C., Finthammer, M., Thimm, M.: Probabilistic Logics in Expert Systems: Approaches, Implementations, and Applications. In: Hameurlain, A., Liddle, S.W., Schewe, K.-D., Zhou, X. (eds.) DEXA 2011, Part I. LNCS, vol. 6860, pp. 27–46. Springer, Heidelberg (2011)
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)
Kern-Isberner, G., Lukasiewicz, T.: Combining probabilistic logic programming with the power of maximum entropy. Artificial Intelligence, Special Issue on Nonmonotonic Reasoning 157(1-2), 139–202 (2004)
Kern-Isberner, G., Thimm, M.: Novel Semantical Approaches to Relational Probabilistic Conditionals. In: Proceedings of the Twelfth International Conference on the Principles of Knowledge Representation and Reasoning, KR 2010, pp. 382–392 (May 2010)
Kern-Isberner, G., Thimm, M.: A ranking semantics for first-order conditionals. In: Proceedings 20th European Conference on Artificial Intelligence, ECAI 2012 (to appear, 2012)
Kersting, K., De Raedt, L.: Bayesian Logic Programming: Theory and Tool. In: Getoor, L., Taskar, B. (eds.) An Introduction to Statistical Relational Learning. MIT Press (2007)
Ketkar, N.S., Holder, L.B., Cook, D.J.: Comparison of Graph-based and Logic-based Multi-relational Data Mining. SIGKDD Explor. Newsl. 7(2), 64–71 (2005)
Kok, S., Singla, P., Richardson, M., Domingos, P., Sumner, M., Poon, H., Lowd, D., Wang, J.: The Alchemy System for Statistical Relational AI: User Manual. Department of Computer Science and Engineering. University of Washington (2008)
Krämer, A., Beierle, C.: On Lifted Inference for a Relational Probabilistic Conditional Logic with Maximum Entropy Semantics. In: Lukasiewicz, T., Sali, A. (eds.) FoIKS 2012. LNCS, vol. 7153, pp. 224–243. Springer, Heidelberg (2012)
Loh, S., Thimm, M., Kern-Isberner, G.: On the problem of grounding a relational probabilistic conditional knowledge base. In: Proceedings of the 14th International Workshop on Non-Monotonic Reasoning, NMR 2010, Toronto, Canada (May 2010)
Loh, S., Thimm, M., Kern-Isberner, G.: On the problem of grounding a relational probabilistic conditional knowledge base. In: Meyer, T., Ternovska, E. (eds.) Proceedings 13th International Workshop on Nonmonotonic Reasoning, NMR 2010. Subworkshop on NMR and Uncertainty (2010)
Muggleton, S.H., Chen, J.: A Behavioral Comparison of Some Probabilistic Logic Models. In: De Raedt, L., Frasconi, P., Kersting, K., Muggleton, S. (eds.) Probabilistic ILP 2007. LNCS (LNAI), vol. 4911, pp. 305–324. Springer, Heidelberg (2008)
Muggleton, S.H.: Stochastic Logic Programs. In: de Raedt, L. (ed.) Advances in Inductive Logic Programming, pp. 254–264. IOS Press, Amsterdam (1996)
Nilsson, N.: Probabilistic logic. Artificial Intelligence 28, 71–87 (1986)
Nute, D., Cross, C.: Conditional Logic. In: Gabbay, D., Guenther, F. (eds.) Handbook of Philosophical Logic, vol. 4, pp. 1–98. Kluwer Academic Publishers (2002)
Paris, J.: The uncertain reasoner’s companion – A mathematical perspective. Cambridge University Press (1994)
Pearl, J.: Fusion, propagation and structuring in belief networks. Artificial Intelligence 29, 241–288 (1986)
Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann (1988)
Raedt, L.D., Dehaspe, L.: Clausal Discovery. Machine Learning 26, 99–146 (1997)
Raedt, L.D., Kimmig, A., Gutmann, B., Kersting, K., Costa, V.S., Toivonen, H.: Probabilistic Inductive Querying Using ProbLog. Technical Report CW 552, Department of Computer Science. Katholieke Universiteit Leuven, Belgium (June 2009)
Richardson, M., Domingos, P.: Markov Logic Networks. Machine Learning 62(1-2), 107–136 (2006)
Robert Koch-Institut: Public Use File KiGGS, Kinder- und Jugendgesundheitssurvey 2003-2006, Berlin (2008)
Rödder, W.: Conditional Logic and the Principle of Entropy. Artificial Intelligence 117, 83–106 (2000)
Rödder, W., Meyer, C.-H.: Coherent Knowledge Processing at Maximum Entropy by SPIRIT. In: Proceedings UAI 1996, pp. 470–476 (1996)
Rödder, W., Reucher, E., Kulmann, F.: Features of the expert-system-shell SPIRIT. Logic Journal of the IGPL 14(3), 483–500 (2006)
Schmaußer-Hechfellner, E.: Probabilistic logic knowledge modelling of statistical medical data by applying learning- and inference-techniques of Markov logic networks. Bachelor Thesis, Dept. of Computer Science, FernUniversität in Hagen (2011) (In German)
Srinivasan, A.: The Aleph Manual (2007), http://www.comlab.ox.ac.uk/activities/machinelearning/Aleph/
Thimm, M., Finthammer, M., Loh, S., Kern-Isberner, G., Beierle, C.: A system for relational probabilistic reasoning on maximum entropy. In: Guesgen, H.W., Murray, R.C. (eds.) Proceedings 23rd International FLAIRS Conference, FLAIRS 2010, pp. 116–121. AAAI Press, Menlo Park (2010)
Thimm, M., Kern-Isberner, G., Fisseler, J.: Relational Probabilistic Conditional Reasoning at Maximum Entropy. In: Liu, W. (ed.) ECSQARU 2011. LNCS, vol. 6717, pp. 447–458. Springer, Heidelberg (2011)
Wellman, M.P., Breese, J.S., Goldman, R.P.: From Knowledge Bases to Decision Models. The Knowledge Engineering Review 7(1), 35–53 (1992)
Yue, A., Liu, W., Hunter, A.: Measuring the Ignorance and Degree of Satisfaction for Answering Queries in Imprecise Probabilistic Logic Programs. In: Greco, S., Lukasiewicz, T. (eds.) SUM 2008. LNCS (LNAI), vol. 5291, pp. 386–400. Springer, Heidelberg (2008)
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Kern-Isberner, G., Beierle, C., Finthammer, M., Thimm, M. (2012). Comparing and Evaluating Approaches to Probabilistic Reasoning: Theory, Implementation, and Applications. In: Hameurlain, A., Küng, J., Wagner, R., Liddle, S.W., Schewe, KD., Zhou, X. (eds) Transactions on Large-Scale Data- and Knowledge-Centered Systems VI. Lecture Notes in Computer Science, vol 7600. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34179-3_2
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