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Numerical uncertainty management in user and student modeling: An overview of systems and issues

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Abstract

A rapidly growing number of user and student modeling systems have employed numerical techniques for uncertainty management. The three major paradigms are those of Bayesian networks, the Dempster-Shafer theory of evidence, and fuzzy logic. In this overview, each of the first three main sections focuses on one of these paradigms. It first introduces the basic concepts by showing how they can be applied to a relatively simple user modeling problem. It then surveys systems that have applied techniques from the paradigm to user or student modeling, characterizing each system within a common framework. The final main section discusses several aspects of the usability of these techniques for user or student modeling, such as their knowledge engineering requirements, their need for computational resources, and the communicability of their results.

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References

  • Ayton, P. and E. Pascoe: 1995, ‘Bias in Human Judgement under Uncertainty?’.The Knowledge Engineering Review 10(1), 21–41.

    Google Scholar 

  • Bauer, M.: 1995, ‘A Dempster-Shafer Approach to Modeling Agent Preferences for Plan Recognition’.User Modeling and User-Adapted Interaction. In this special issue.

  • Bauer, M.: 1996, ‘Acquisition of User Preferences for Plan Recognition’. In:Proceedings of the Fifth International Conference on User Modeling. Kailua-Kona, HI.

  • Besnard, P. and S. Hanks (eds.): 1995,Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence. San Francisco: Morgan Kaufmann.

    Google Scholar 

  • Carberry, S.: 1990, ‘Incorporating Default Inferences into Plan Recognition’. In:Proceedings of the Eight National Conference on Artificial Intelligence. Boston, MA, pp. 471–478.

  • Carbonaro, A., V. Maniezzo, M. Roccetti, and P. Salomoni: 1995, ‘Modelling the Student in Pitagora 2.0’.User Modeling and User-Adapted Interaction 4, 233–251.

    Google Scholar 

  • Chandrasekaran, B.: 1994, ‘Broader Issues at Stake: A Response to Elkan’.IEEE Expert 9(4), 10–13.

    Google Scholar 

  • Charniak, E.: 1991, ‘Bayesian Networks without Tears’.AI Magazine 12(4), 50–63.

    Google Scholar 

  • Charniak, E. and R. Goldman: 1991, ‘A Probabilistic Model of Plan Recognition’. In:Proceedings of the Ninth National Conference on Artificial Intelligence. Anaheim, CA, pp. 160–165.

  • Charniak, E. and R. P. Goldman: 1993, ‘A Bayesian Model of PlanRecognition’.Artifcial Intelligence 64, 53–79.

    Google Scholar 

  • Chin, D. N.: 1989, ‘KNOME: Modeling What the User Knows in UC’. In: A. Kobsa and W. Wahlster (eds.):User Models in Dialog Systems. Berlin: Springer, pp. 74–107.

    Google Scholar 

  • Conati, C. and K. VanLehn: 1996, ‘POLA: A Student Modeling Framework for Probabilistic OnLine Assessment of Problem Solving Performance’. In:Proceedings of the Fifth International Conference on User Modeling. Kailua-Kona, HI.

  • Cox, E.: 1994,The Fuzzy Systems Handbook: A Practitioner's Guide to Building, Using, and Maintaining Fuzzy Systems. Boston: AP Professional.

    Google Scholar 

  • de Rosis, F., S. Pizzutilo, A. Russo, D. C. Berry, and F. J. N. Molina: 1992, ‘Modeling the User Knowledge by Belief Networks’.User Modeling and User-Adapted Interaction 2, 367–388.

    Google Scholar 

  • Delcher, A. L., A. Grove, S. Kasif, and J. Pearl: 1995, ‘Logarithmic-Time Updates and Queries in Probabilistic Networks’. In: P. Besnard and S. Hanks (eds.):Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence. San Francisco: Morgan Kaufmann, pp. 116–124.

    Google Scholar 

  • Dempster, A. P. and A. Kong: 1988, ‘Uncertain Evidence and Artificial Analysis’.Journal of Statistical Planning and Inference 20, 355–368. Reprinted in collection by Shafer and Pearl (1990).

    Google Scholar 

  • Desmarais, M. C., A. Maluf, and J. Liu: 1995, ‘User-Expertise Modeling with Empirically Derived Probabilistic Implication Networks’.User Modeling and User-Adapted Interaction. In this special issue.

  • Draney, K. L., P. Pirolli, and M. Wilson: 1995, ‘A Measurement Model for a Complex Cognitive Skill’. In: P. D. Nichols, S. F. Chipman, and R. L. Brennan (eds.):Cognitively Diagnostic Assessment. Hillsdale, NJ: Erlbaum, pp. 103–125.

    Google Scholar 

  • Druzdzel, M., L. van der Gaag, M. Henrion, and F. Jensen: 1995, ‘Building Probabilistic Networks: Where Do the Numbers Come From?’. Working notes of a workshop held in conjunction with the Fourteenth International Joint Conference on Artificial Intelligence.

  • Druzdzel, M. J. and L. C. van der Gaag: 1995, ‘Elicitation of Probabilities for Belief Networks: Combining Qualitative and Quantitative Information’. In: P. Besnard and S. Hanks (eds.):Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence. San Francisco: Morgan Kaufmann, pp. 141–148.

    Google Scholar 

  • Dubois, D., H. Prade, and R. R. Yager (eds.): 1993,Readings in Fuzzy Sets for Intelligent Systems. San Mateo, CA: Morgan Kaufmann.

    Google Scholar 

  • Elkan, C.: 1994, ‘The Paradoxical Success of Fuzzy Logic’.IEEE Expert 9(4), 3–8.

    Google Scholar 

  • Falmagne, J.-C., M. Koppen, M. Villano, J.-P. Doignon, and L. Johannesen: 1990, ‘Introduction to Knowledge Spaces: How to Build, Test, and Search Them’.Psychological Review 97, 201–224.

    Google Scholar 

  • Fiske, S. T. and S. E. Taylor: 1991,Social Cognition. New York: McGraw-Hill. 2nd edition.

    Google Scholar 

  • Forbes, J., T. Huang, K. Kanazawa, and S. Russell: 1995, ‘The BATmobile: Towards a Bayesian Automated Taxi’. In: C. S. Mellish (ed.):Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence. San Mateo, CA: Morgan Kaufmann, pp. 1878–1885.

    Google Scholar 

  • Freksa, C.: 1994, ‘Fuzzy Logic: An Interface Between Logic and Human Reasoning’.IEEE Expert 9(4), 20–21.

    Google Scholar 

  • Gordon, J. and E. H. Shortliffe: 1984, ‘The Dempster-Shafer Theory of Evidence’. In:B. G. Buchanan and E. H. Shortliffe (eds.):Rule-Based Expert Systems: The MYCIN Experiments of the Stanford Heuristic Programming Project. Reading: MA: Addison-Wesley.

    Google Scholar 

  • Hambleton, R. K. and H. Swaminathan: 1985,Item Response Theory: Principles and Applications. Boston: Kluwer-Nijhoff.

    Google Scholar 

  • Hawkes, L. W., S. J. Derry, and E. A. Rundensteiner: 1990, ‘Individualized Tutoring Using an Intelligent Fuzzy Temporal Relational Database’.International Journal of Man-Machine Studies 33, 409–429.

    Google Scholar 

  • Heckerman, D., D. Geiger, and D. M. Chickering: 1994, ‘Learning Bayesian Networks: The Combination of Knowledge and Statistical Data’. In: R. Lopez de Mantaras and D. Poole (eds.):Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence. San Francisco: Morgan Kaufmann, pp. 293–301.

    Google Scholar 

  • Henrion, M. and M. J. Druzdzel: 1991, ‘Qualitative Propagation and Scenario-Based Schemes for Explaining Probabilistic Reasoning’. In: P. P. Bonissone, M. Henrion, L. N. Kanal, and J. F. Lemmer (eds.):Uncertainty in Artificial Intelligence 6. Amsterdam: Elsevier, pp. 17–32.

    Google Scholar 

  • Henrion, M., G. Provan, B. D. Favero, and G. Sanders: 1994, ‘An Experimental Comparison of Numerical and Qualitative Probabilistic Reasoning’. In: R. Lopez de Mantaras and D. Poole (eds.):Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence. San Francisco: Morgan Kaufmann, pp. 319–326.

    Google Scholar 

  • Herzog, C.: 1994, ‘Fuzzy-Techniken für das Verstehen von Studentenlösungen in intelligenten Lehrsystemen [Fuzzy Techniques for Understanding Student Solutions in Intelligent Tutoring Systems]’. In: R. Gunzenhäuser, C. Möbus, and D. Rösner (eds.):Papers for the Seventh Meeting of GI Section 1.1.5/7.0.1, “Intelligent Tutoring Systems”. Ulm, Germany: Research Institute for Application-Oriented Knowledge Processing (FAW). Proceedings available as FAW Technical Report FAW-TR-94003.

    Google Scholar 

  • Horvitz, E. and M. Barry: 1995, ‘Display of Information for Time-Critical Decision Making’. In: P. Besnard and S. Hanks (eds.):Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence. San Francisco: Morgan Kaufmann, pp. 296–314.

    Google Scholar 

  • Huber, M. J., E. H. Durfee, and M. P. Wellman: 1994, ‘The Automated Mapping of Plans for Plan Recognition’. In: R. Lopez de Mantaras and D. Poole (eds.):Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence. San Francisco: Morgan Kaufmann, pp. 344–351.

    Google Scholar 

  • Hustadt, U. and A. Nonnengart: 1993, ‘Modalities in Knowledge Representation’. In:Proceedings of the Sixth Australian Joint Conference on Artificial Intelligence. Sydney, pp. 249–254.

  • Jameson, A.: 1992, ‘Generalizing the Double-Stereotype Approach: A Psychological Perspective’. In: E. André, R. Cohen, W. Graf, B. Kass, C. Paris, and W. Wahlster (eds.):Proceedings of the Third International Workshop on User Modeling. Dagstuhl, Germany, pp. 69–83. Proceedings available as Report DFKI-D-92-17 of the German Research Center for Artificial Intelligence, Saarbrücken.

  • Jameson, A.: 1995, ‘Logic Is Not Enough: Why Reasoning About Another Person's Beliefs Is Reasoning Under Uncertainty’. In: A. Laux and H. Wansing (eds.):Knowledge and Belief in Philosophy and Artificial Intelligence. Berlin: Akademie Verlag, pp. 199–229.

    Google Scholar 

  • Jameson, A., R. Schäfer, J. Simons, and T. Weis: 1995, ‘Adaptive Provision of Evaluation-Oriented Information: Tasks and Techniques’. In: C. S. Mellish (ed.):Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence. San Mateo, CA: Morgan Kaufmann, pp. 1886–1893.

    Google Scholar 

  • Kambouri, M., M. Koppen, M. Villano, and J.-C. Falmagne: 1994, ‘Knowledge Assessment: Tapping Human Expertise by the QUERY Routine’.International Journal of Human-Computer Studies 40, 119–151.

    Google Scholar 

  • Katz, S. and A. Lesgold: 1992, ‘Approaches to Student Modeling in the Sherlock Tutors’. In: E. André, R. Cohen, W. Graf, B. Kass, C. Paris, and W. Wahlster (eds.):Proceedings of the Third International Workshop on User Modeling. Dagstuhl, Germany, pp. 205–230. Available as Report DFKI-D-92-17 of the German Research Center for Artificial Intelligence, Saarbrücken.

  • Katz, S., A. Lesgold, G. Eggan, and M. Gordin: 1992, ‘Modeling the Student in Sherlock II’.Journal of Artificial Intelligence in Education 3, 495–518.

    Google Scholar 

  • Kipper, B. and A. Jameson: 1994, ‘Semantics and Pragmatics of Vague Probability Expressions’. In:Proceedings of the Sixteenth Annual Conference of the Cognitive Science Society. Atlanta, pp. 496–501.

  • Klein, D. A. and E. H. Shortliffe: 1994, ‘A Framework for Explaining Decision-Theoretic Advice’.Artificial Intelligence 67, 201–243.

    Google Scholar 

  • Kölln, M. E.: 1995, ‘Employing User Attitudes in Text Planning’. In:Proceedings of the Fifth European Workshop on Natural Language Generation. Leiden, The Netherlands, pp. 163–179.

  • Kosko, B.: 1992,Neural Networks and Fuzzy Systems: A Dynamical Systems Approach to Machine Intelligence. London: Prentice-Hall.

    Google Scholar 

  • Kreinovich, V. Y., A. Bernat, W. Borrett, Y. Mariscal, and E. Villa: 1994, ‘Monte-Carlo Methods Make Dempster-Shafer Formalism Feasible’. In: R. R. Yager, J. Kacprzyk, and M. Fedrizzi (eds.):Advances in the Dempster-Shafer Theory of Evidence. New York: Wiley, pp. 175–191.

    Google Scholar 

  • Kruse, R., E. Schwecke, and J. Heinsohn: 1991,Uncertainty and Vagueness in Knowledge Based Systems: Numerical Methods. Berlin: Springer.

    Google Scholar 

  • Lamata, M. T. and S. Moral: 1994, ‘Calculus with Linguistic Probabilities and Beliefs’. In: R. R. Yager, J. Kacprzyk, and M. Fedrizzi (eds.):Advances in the Dempster-Shafer Theory of Evidence. New York: Wiley, pp. 133–152.

    Google Scholar 

  • Lopez de Mantaras, R. and D. Poole (eds.): 1994,Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence. San Francisco: Morgan Kaufmann.

    Google Scholar 

  • Maes, P.: 1994, ‘Agents That Reduce Work and Information Overload’.Communications of the ACM 37(7), 30–40.

    Google Scholar 

  • Martin, J. D. and K. VanLehn: 1993, ‘OLAE: Progress Toward a Multi-Activity, Bayesian Student Modeler’. In: P. Brna, S. Ohlsson, and H. Pain (eds.):Artificial Intelligence in Education: Proceedings of AI-ED 93. Charlottesville, VA: Association for the Advancement of Computing in Education, pp. 410–417.

    Google Scholar 

  • Martin, J. D. and K. VanLehn: 1995, ‘A Bayesian Approach to Cognitive Assessment’. In: P. D. Nichols, S. F. Chipman, and R. L. Brennan (eds.):Cognitively Diagnostic Assessment. Hillsdale, NJ: Erlbaum, pp. 141–165.

    Google Scholar 

  • Mislevy, R. J.: 1994, ‘Evidence and Inference in Educational Assessment’.Psychometrika 59, 439–483.

    Google Scholar 

  • Mislevy, R. J. and D. H. Gitomer: 1995, ‘The Role of Probability-Based Inference in an Intelligent Tutoring System’.User Modeling and User-Adapted Interaction. In this special issue.

  • Neapolitan, R. E.: 1990,Probabilistic Reasoning in Expert Systems: Theory and Algorithms. New York: Wiley.

    Google Scholar 

  • Nisbett, R. and L. Ross: 1980,Human Inference: Strategies and Shortcomings of Social Judgment. Englewood Cliffs, NJ: Prentice-Hall.

    Google Scholar 

  • Orwant, J.: 1995, ‘Heterogeneous Learning in the Doppelgänger User Modeling System’.User Modeling and User-Adapted Interaction 4(2), 107–130.

    Google Scholar 

  • Pearl, J.: 1988,Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. San Mateo, CA: Morgan Kaufmann.

    Google Scholar 

  • Petrushin, V. A. and K. M. Sinitsa: 1993, ‘Using Probabilistic Reasoning Techniques for Learner Modeling’. In: P. Brna, S. Ohlsson, and H. Pain (eds.):Artificial Intelligence in Education: Proceedings of AI-ED 93. Charlottesville, VA: Association for the Advancement of Computing in Education, pp. 418–425.

    Google Scholar 

  • Petrushin, V. A., K. M. Sinitsa, and V. Zherdienko: 1995, ‘Probabilistic Approach to Adaptive Students’ Knowledge Assessment: Methodology and Experiment’. In: J. Greer (ed.):Artificial Intelligence in Education: Proceedings of AI-ED 95. Charlottesville VA: Association for the Advancement of Computing in Education, pp. 51–58.

    Google Scholar 

  • Popp, H. and D. Lödel: 1995, ‘Fuzzy Techniques and User Modeling in Sales Assistants’.User Modeling and User-Adapted Interaction. In this special issue.

  • Pynadath, D. V. and M. P. Wellman: 1995, ‘Accounting for Context in Plan Recognition, with Application to Traffic Monitoring’. In: P. Besnard and S. Hanks (eds.):Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence. San Francisco: Morgan Kaufmann, pp. 472–481.

    Google Scholar 

  • Quinlan, J. R.: 1983, ‘Learning Efficient Classification Procedures and Their Application to Chess End Games’. In: R. Michalski, J. Carbonell, and T. Mitchell (eds.):Machine Learning: An Artificial Intelligence Approach. Berlin: Springer, pp. 463–482.

    Google Scholar 

  • Raskutti, B. and I. Zukerman: 1991, ‘Handling Uncertainty During Plan Recognition in Task-Oriented Consultation Systems’. In: B. D. D'Ambrosio, P. Smets, and P. P. Bonissone (eds.):Uncertainty in Artificial Intelligence: Proceedings of the Seventh Conference. San Mateo, CA: Morgan Kaufmann, pp. 308–315.

    Google Scholar 

  • Roccetti, M. and P. Salomoni: 1995, ‘Using Bayesian Belief Networks for the Automated Assessment of Students' Knowledge of Geometry Solving Procedures’. Manuscript submitted for publication.

  • Russell, S., J. Binder, D. Koller, and K. Kanazawa: 1995, ‘Local Learning in Probabilistic Networks with Hidden Variables’. In: C. S. Mellish (ed.):Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence. San Mateo, CA: Morgan Kaufmann, pp. 1146–1152.

    Google Scholar 

  • Russell, S. J. and P. Norvig: 1995,Artificial Intelligence: A Modern Approach. Englewood Cliffs, NJ: Prentice-Hall.

    Google Scholar 

  • Schäfer, R.: 1994, ‘Multidimensional Probabilistic Assessment of Interest and Knowledge in a Noncooperative Dialog Situation’. In: C. G. Thomas (ed.):Proceedings of ABIS-94: GI Workshop on Adaptivity and User Modeling in Interactive Software Systems. Sankt Augustin, Germany, pp. 46–62.

  • Shafer, G. and J. Pearl (eds.): 1990,Readings in Uncertain Reasoning. San Mateo, CA: Morgan Kaufmann.

    Google Scholar 

  • Shafer, G. and A. Tversky: 1985, ‘Languages and Designs for Probability Judgment’.Cognitive Science 9, 177–210.

    Google Scholar 

  • Shenoy, P. P.: 1994, ‘Using Dempster-Shafer's Belief Function Theory in Expert Systems’. In: R. R. Yager, J. Kacprzyk, and M. Fedrizzi (eds.):Advances in the Dempster-Shafer Theory of Evidence. New York: Wiley, pp. 395–414.

    Google Scholar 

  • Sheth, B. and P. Maes: 1993, ‘Evolving Agents for Personalized Information Filtering’. In:Proceedings of the Ninth Conference on Artificial Intelligence for Applications, CAIA-93. Orlando, FL, pp. 345–352.

  • Sime, J.-A.: 1993, ‘Modelling a Learner's Multiple Models with Bayesian Belief Networks’. In: P. Brna, S. Ohlsson, and H. Pain (eds.):Artificial Intelligence in Education: Proceedings of AI-ED 93. Charlottesville, VA: Association for the Advancement of Computing in Education, pp. 426–432.

    Google Scholar 

  • Tokuda, N. and A. Fukuda: 1993, ‘A Probabilistic Inference Scheme for Hierarchical Buggy Models’.International Journal of Man-Machine Studies 38, 857–872.

    Google Scholar 

  • Vadiee, N. and M. Jamshidi: 1994, ‘The Promising Future of Fuzzy Logic’.IEEE Expert 9(4), 36–38.

    Google Scholar 

  • van Beek, P.: 1996, ‘An Investigation of Probabilistic Interpretations of Heuristics in Plan Recognition’. In:Proceedings of the Fifth International Conference on User Modeling. Kailua-Kona, HI.

  • van Mulken, S.: 1996, ‘Reasoning About the User's Decoding of Presentations in an Intelligent Multimedia Presentation System’. In:Proceedings of the Fifth International Conference on User Modeling. Kailua-Kona, HI.

  • Villano, M.: 1992, ‘Probabilistic Student Models: Bayesian Belief Networks and Knowledge Space Theory’. In: C. Frasson, G. Gauthier, and G. I. McCalla (eds.):Intelligent Tutoring Systems: Proceedings of the Second International Conference, ITS'92. Berlin: Springer, pp. 491–498.

    Google Scholar 

  • von Winterfeldt, D. and W. Edwards: 1986,Decision Analysis and Behavioral Research. Cambridge, England: Cambridge University Press.

    Google Scholar 

  • Wahlster, W., E. André, W. Finkler, H.-J. Profitlich, and T. Rist: 1993, ‘Plan-Based Integration of Natural Language and Graphics Generation’.Artificial Intelligence 63, 387–427.

    Google Scholar 

  • Wallsten, T. S. and D. V. Budescu: 1995, ‘A Review of Human Linguistic Probability Processing: General Principles and Empirical Evidence’.The Knowledge Engineering Review 10(1), 43–62.

    Google Scholar 

  • Wallsten, T. S., D. V. Budescu, R. Zwick, and S. M. Kemp: 1993, ‘Preferences and Reasons for Communicating Probabilistic Information in Verbal or Numerical Terms’.Bulletin of the Psychonomic Society 31, 135–138.

    Google Scholar 

  • Wellman, M. P. and C.-L. Liu: 1995, ‘State-Space Abstraction for Anytime Evaluation of Probabilistic Networks’. In: P. Besnard and S. Hanks (eds.):Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence. San Francisco: Morgan Kaufmann, pp. 567–574.

    Google Scholar 

  • Xu, H. and P. Smets: 1995, ‘Generating Explanations for Evidential Reasoning’. In: P. Besnard and S. Hanks (eds.):Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence. San Francisco: Morgan Kaufmann, pp. 574–581.

    Google Scholar 

  • Yager, R. R.: 1992, ‘Expert Systems Using Fuzzy Logic’. In: R. R. Yager and L. A. Zadeh (eds.):An Introduction to Fuzzy Logic Applications in Intelligent Systems. Boston: Kluwer, pp. 27–44.

    Google Scholar 

  • Yager, R. R., J. Kacprzyk, and M. Fedrizzi (eds.): 1994,Advances in the Dempster-Shafer Theory of Evidence. New York: Wiley.

    Google Scholar 

  • Yager, R. R. and L. A. Zadeh (eds.): 1992,An Introduction to Fuzzy Logic Applications in Intelligent Systems. Boston: Kluwer.

    Google Scholar 

  • Zadeh, L. A.: 1981, ‘Possibility Theory and Soft Data Analysis’. In: L. Cobb and R. Thrall (eds.):Mathematical Frontiers of Social and Policy Sciences. Boulder, CO: Westview Press, pp. 69–129.

    Google Scholar 

  • Reprinted in collection by Dubois et al. (1993).

  • Zadeh, L. A.: 1994, ‘Fuzzy Logic, Neural Networks, and Soft Computing’.Communications of the ACM37(3), 77–84.

    Google Scholar 

  • Zarley, D., Y.-T. Hsia, and G. Shafer: 1988, ‘Evidential Reasoning Using DELIEF’. In:Proceedings of the Seventh National Conference on Artificial Intelligence. St. Paul, MN, pp. 205–209. Reprinted in collection by Shafer and Pearl (1990).

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Jameson, A. Numerical uncertainty management in user and student modeling: An overview of systems and issues. User Model User-Adap Inter 5, 193–251 (1995). https://doi.org/10.1007/BF01126111

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