{"type":"ScholarlyArticle","title":"Learning to Reason: The Non-Monotonic Case","authors":[{"name":"Dan Roth","slug":"dan-roth","given":"Dan","family":"Roth","affiliation":"Division of Applied Sciences , Harvard University , Cambridge , MA 02138 ."}],"abstract":"We suggest a new approach for the study of the nonmonotonicity of human commonsense reasoning. The two main premises that underlie this work are that commonsense reasoning is an inductive phenomenon, and that missing information in the interaction of the agent with the environment may be as informative for future interactions as observed information. This intuition is formalized and the problem of reasoning from incomplete information is presented as a problem of learning attribute functions over a generalized domain. We consider examples that illustrate various aspects of the non-monotonic reasoning phenomena, which have been used over the years as \"bench-marks\" for various formalisms, and translate them into Learning to Reason problems. We demonstrate that these have concise representations over the generalized domain and prove that these representations can be learned efficiently. The framework developed suggests an \"operational\" approach to studying reasoning that is nevertheless rigorous and amenable to analysis. We show that this approach efficiently supports reasoning with incomplete information and at the same time matches our expectations of plausible patterns of reasoning in cases where other theories do not. This work continues previous works in the Learning to Reason framework, and supports the thesis that in order to develop a computational account for commonsense reasoning one should study the phenomena of learning and reasoning together.","doi":null,"url":"https://ijcai.org/proceedings/1995/152","pdf":"https://ijcai.org/proceedings/1995/0152.pdf","markdown":"https://ijcai.org/proceedings/1995/152.md","bibtex":"https://ijcai.org/proceedings/1995/bibtex/152","volume":{"slug":"1995","title":"Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 1995","url":"https://ijcai.org/proceedings/1995/","year":1995,"location":"Montréal, Québec, Canada","dates":"","editors":"Chris S. Mellish","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Learning","track":"Learning","number":152,"pages":{"first":1178,"last":1183},"keywords":[],"videos":[],"references":[{"position":1,"raw":"[AI, 1980] AI. Special issue on non-monotonic logic. Artificial Intelligence, 13(1 ,2), 1980.","title":"AI. Special issue on non-monotonic logic","authors":"Ai","year":"1980","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Angluin and Laird, 1988] D. Angluin and P. Laird. Learning from noisy examples. Machine Learning, 2(4):343-370, 1988.","title":"Learning from noisy examples","authors":"D Angluin, P Laird","year":"1988","venue":"Machine Learning","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Angluin, 1988] D. Angluin. Queries and concept learning. Ma- chine Learning, 2(4):319-342, Aprill988.","title":"Queries and concept learning","authors":"D Angluin","year":null,"venue":"Machine Learning","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Bacchus et al., 1993] F. Bacchus, A. Grove, J. Y. Halpern, and D. Koller. Statistical foundations for default reasoning. In Pro- ceedings of the International Joint Conference of Artificial Intel- ligence, pages 563-569, 1993.","title":"Statistical foundations for default reasoning","authors":"F Bacchus, A Grove, J Y Halpern, D Koller","year":"1993","venue":"Proceedings of the International Joint Conference of Artificial Intelligence","doi":null,"url":null,"internal_url":"/proceedings/1993/79"},{"position":5,"raw":"[Blum et al., 1994] A. Blum, R. Khardon, A. Kushilevitz, L. Pitt, and D. Roth. On learning read-k satisfy-j DNF. In Proceedings of the Annual ACM Workshop on Computational Learning Theory, pages 110-117, 1994. (Submitted for publication).","title":"On learning read-k satisfy-j DNF","authors":"A Blum, R Khardon, A Kushilevitz, L Pitt, D Roth","year":"1994","venue":"Proceedings of the Annual ACM Workshop on Computational Learning Theory","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Bshouty, 1993] N. H. Bshouty. Exact learning via the monotone theory. In Proceedings of the IEEE Symp. on Foundation of Computer Science, pages 302-311, Palo Alto, CA., 1993.","title":"Exact learning via the monotone theory","authors":"N H Bshouty","year":"1993","venue":"Proceedings of the IEEE Symp. on Foundation of Computer Science","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Etherington, 1988] D. W. Etherington. Reasoning With Incomplete Information. Morgan Kaufmann, 1988.","title":"Reasoning With Incomplete Information","authors":"D W Etherington","year":"1988","venue":null,"doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Geffner, 1990] H. Geffner. Default Reasoning: Casual and Con- ditional Theories. MIT Press, 1990.","title":"Default Reasoning: Casual and Conditional Theories","authors":"H Geffner","year":"1990","venue":null,"doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Geffner, 1994] H. Geffner. Causal default reasoning: Principles and algorithms. In Proceedings of the National Conference on Artificial Intelligence, pages 245-250, 1994.","title":"Causal default reasoning: Principles and algorithms","authors":"H Geffner","year":"1994","venue":"Proceedings of the National Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Goldszmidt and Pearl, 1991] M. Goldszmidt and J. Pearl. System Z+: A formalism for reasoning with variable strength defaults. In Proceedings of the National Conference on Artificial Intelligence, pages 399-404, 1991.","title":"System Z+: A formalism for reasoning with variable strength defaults","authors":"M Goldszmidt, J Pearl","year":"1991","venue":"Proceedings of the National Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Hanks and McDermott, 1986] S. Hanks and D. McDermott. De- fault reasoning, nonmonotonic logics, and the frame problem. In Proceedings of the National Conference on Artificial Intelligence, pages328-333, 1986.","title":"Default reasoning, nonmonotonic logics, and the frame problem","authors":"S Hanks, D Mcdermott","year":"1986","venue":"Proceedings of the National Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Kearns, 1993] M. Kearns. Efficient noise-tolerant learning from statistical queries. In Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing, pages 392-401 , 1993 .","title":"Efficient noise-tolerant learning from statistical queries","authors":"M Kearns","year":"1993","venue":"Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Khardon and Roth, 1994a] R. Khardon and D. Roth. Exploiting relevance through model-based reasoning. In AAAI Fall Sympo- sium on Relevance, pages 109-114, 1994.","title":"Exploiting relevance through model-based reasoning","authors":"Roth ; Khardon, R Khardon, D Roth","year":"1994","venue":"AAAI Fall Symposium on Relevance","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Khardon and Roth, 1994b] R. Khardon and D. Roth. Learning to reason. In Proceedings of the National Conference on Artifi- cial Intelligence, pages 682-687, 1994. Full version: TR-02-94, Aiken Computation Lab., Harvard University, January 1994.","title":"Learning to reason","authors":"Roth ; Khardon, R Khardon, D Roth","year":"1994","venue":"Proceedings of the National Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Khardon and Roth, 1995a] R. Khardon and D. Roth. Default- reasoning with models. In Proceedings of the International Joint Conference of Artificial Intelligence, August 1995.","title":"Defaultreasoning with models","authors":"Roth ; Khardon, R Khardon, D Roth","year":"1995","venue":"Proceedings of the International Joint Conference of Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Khardon and Roth, 1995b] R. Khardon and D. Roth. Learning to reason with a restricted view. In Workshop on Computational Learning Theory, July 1995.","title":"Learning to reason with a restricted view","authors":"Roth ; Khardon, R Khardon, D Roth","year":"1995","venue":"Workshop on Computational Learning Theory","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Kraus et al., 1990] S. Kraus, D. Lehmann, and M. Magidor. Pref- erential models and cumulative logics. Artificial Intelligence , 44:167-207, 1990.","title":"Preferential models and cumulative logics","authors":"S Kraus, D Lehmann, M Magidor","year":"1990","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Kushilevitz and Roth, 1995] E. Kushilevitz and D. Roth. On learn- ing visual concepts and DNF formulae. Machine Learning, I (1 ): 11-46, 1995. Earlier version appeared in Proceedings of the ACM Workshop on Computational Learning Theory '93.","title":"On learning visual concepts and DNF formulae","authors":"E Kushilevitz, D Roth","year":"1995","venue":"Proceedings of the ACM Workshop on Computational Learning Theory '93","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Littles tone, 1989] N. Littles tone. Mistake bounds and logarithmic linear-threshold learning algorithms. PhD thesis, U. C. Santa Cruz, March 1989.","title":"Mistake bounds and logarithmic linear-threshold learning algorithms","authors":"N Littles Tone","year":"1989","venue":null,"doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[McCarthy and Hayes, 1969] J. McCarthy and P. Hayes . Some philosophical problems from the standpoint of artificial intelli- gence. In B. Meltzer and D. Michie, editors, Machine Intelligence 4. Edinburgh University Press, 1969.","title":"Some philosophical problems from the standpoint of artificial intelligence","authors":"J Mccarthy, P Hayes","year":"1969","venue":"Machine Intelligence 4","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[McCarthy, 1980] J. McCarthy. Circumscription -a form of non- monotonic reasoning. Artificial Intelligence, 13(1 ,2), 1980.","title":"Circumscription -a form of nonmonotonic reasoning","authors":"J Mccarthy","year":"1980","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Minsky, 1975] M. Minsky. A framework for representing knowl- edge. In P. Winston, editor, The Psychology of Computer Vision .","title":"A framework for representing knowledge","authors":"M Minsky","year":null,"venue":"The Psychology of Computer Vision","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"McGraw-Hill, 1975. Also in R. Brachman and H. Levesque, Readings in Knowledge Representation, 1985.","title":"Readings in Knowledge Representation","authors":"Mcgraw-Hill","year":"1975","venue":null,"doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Neufeld, 1989] E. Neufeld. Default and probabilities; extensions and coherence. In Proceedings of the International Conference on the Principles of Knowledge Representation and Reasoning, pages 312-323, 1989.","title":"Default and probabilities; extensions and coherence","authors":"E Neufeld","year":"1989","venue":"Proceedings of the International Conference on the Principles of Knowledge Representation and Reasoning","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Papadimitriou, 1991] C. H. Papadimitriou. On selecting a satisfy- ing truth assignment. In Proc. 32nd Ann. IEEE Symp. on Foun- dations of Computer Science, pages 163-169, 1991 .","title":"On selecting a satisfying truth assignment","authors":"C H Papadimitriou","year":"1991","venue":"Proc. 32nd Ann. IEEE Symp. on Foundations of Computer Science","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Pearl, 1988] J. Pearl. Probabilistic Reasoning in Intelligent Sys - tems: Networks of Plausible Inference. Morgan Kaufman, 1988.","title":"Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference","authors":"J Pearl","year":"1988","venue":null,"doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Poole, 1989] D. Poole. What the lottery paradox tells us about default reasoning. In Proceedings of the International Conference on the Principles of Knowledge Representation and Reasoning, pages 333-340, 1989.","title":"What the lottery paradox tells us about default reasoning","authors":"D Poole","year":"1989","venue":"Proceedings of the International Conference on the Principles of Knowledge Representation and Reasoning","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[ReiterandG., 1981] R. Reiter and Criscuolo G. On interacting defaults. In Proceedings of the International Joint Conference of Artificial Intelligence, pages 270-276, 1981.","title":"On interacting defaults","authors":"R Reiter, G Criscuolo","year":"1981","venue":"Proceedings of the International Joint Conference of Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Reiter, 1980] R. Reiter. A logic for default reasoning. Artificial Intelligence, 13(1 ,2), 1980.","title":"A logic for default reasoning","authors":"R Reiter","year":"1980","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Reiter, 1987] R. Reiter. Nonmonotonic reasoning. In Annual Re- views of Computer Science, pages 147-188. 1987.","title":"Nonmonotonic reasoning","authors":"R Reiter","year":"1987","venue":"Annual Reviews of Computer Science","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Roth, 1993] D. Roth. On the hardness of approximate reasoning. In Proceedings of the International Joint Conference of Artificial Intelligence, pages 613-618, August 1993. To Appear in Artificial Intelligence Journal, 1995.","title":"On the hardness of approximate reasoning","authors":"D Roth","year":"1993","venue":"Proceedings of the International Joint Conference of Artificial Intelligence","doi":null,"url":null,"internal_url":"/proceedings/1993/86"},{"position":32,"raw":"[Roth, 1995] D. Roth. Learning to reason: the non-monotonic case. 1995. Full Version. In Preparation.","title":"Learning to reason: the non-monotonic case","authors":"D Roth","year":"1995","venue":null,"doi":null,"url":null,"internal_url":null},{"position":33,"raw":"[Schuurmans and Greiner, 1994] D. Schuurmans and R. Greiner. Learning default concepts. In Proceedings of the Tenth Cana- dian Conference on Artificial Intelligence (CSCSI-94 ), 1994.","title":"Learning default concepts","authors":"D Schuurmans, R Greiner","year":"1994","venue":"Proceedings of the Tenth Canadian Conference on Artificial Intelligence (CSCSI-94 )","doi":null,"url":null,"internal_url":null},{"position":34,"raw":"[Selman and Kautz, 1990] B. Selman and H. Kautz. Model- preference default theories. Artificial Intelligence , 45 :287-322, 1990.","title":"Modelpreference default theories","authors":"B Selman, H Kautz","year":"1990","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":35,"raw":"[Selman, 1990] B. Selman. Tractable Default Reasoning . PhD thesis, Department of Computer Science, University of Toronto, 1990.","title":"Tractable Default Reasoning","authors":"B Selman","year":"1990","venue":null,"doi":null,"url":null,"internal_url":null},{"position":36,"raw":"[Touretzky et al., 1987] D. Touretzky, J. Horty, and R. Thomason. A clash of intuitions: The current state of nonmonotonic multiple inheritance systems. In Proceedings of the International Joint Conference of Artificial Intelligence. Morgan Kaufman, 1987.","title":"A clash of intuitions: The current state of nonmonotonic multiple inheritance systems","authors":"D Touretzky, J Horty, R Thomason","year":"1987","venue":"Proceedings of the International Joint Conference of Artificial Intelligence","doi":null,"url":null,"internal_url":"/proceedings/1987/94"},{"position":37,"raw":"[Touretzky, 1986] D. Touretzky. The Mathematics of Inheritance Systems. Morgan Kaufman, 1986.","title":"The Mathematics of Inheritance Systems","authors":"D Touretzky","year":"1986","venue":null,"doi":null,"url":null,"internal_url":null},{"position":38,"raw":"[Valiant, 1984] L. G. Valiant. A theory of the learnable. Communi- cations of the ACM, 27(11 ): 1134-1142, November 1984.","title":"A theory of the learnable","authors":"L G Valiant","year":"1984","venue":"Communications of the ACM","doi":null,"url":null,"internal_url":null},{"position":39,"raw":"L. G. Valiant. Circuits of the Mind. Oxford Uni- versity Press, November 1994.","title":"Circuits of the Mind","authors":"L G Valiant","year":"1994","venue":null,"doi":null,"url":null,"internal_url":null},{"position":40,"raw":"L. G. Valiant. Rationality. Technical Report TR- 32-94, Aiken Computation Lab., Harvard University, November 1994.","title":"Rationality","authors":"L G Valiant","year":"1994","venue":null,"doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}