Abstract
In the seminal paper [6], Gerd Brewka argued that ranking a set of default rules without prerequisites, and selecting extensions according to a lexicographic refinement of the inclusion ordering proves to be a natural, simple and efficient way of dealing with the multiple extension (or “subtheories”) problem. This natural idea has been reused, discussed, revisited, reinvented, adapted many times in the AI community and beyond. Preferred subtheories do not only have an interest in default reasoning, but also in reasoning about time, reasoning by analogy, reasoning with compactly represented preferences, judgment aggregation, and voting. They have several variants (but arguably not so many). In this short paper I will say as much as I can about preferred subtheories in sixteen pages.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Adams, E.W.: The Logic of Conditionals. Reiter, Dordrecht (1975)
Asher, N., Lang, J.: When nonmonotonicity comes from distances. In: KI-94: Advances in Artificial Intelligence, Proceedings of the 18th Annual German Conference on Artificial Intelligence, Saarbrücken, Germany, September 18-23, pp. 308–318 (1994)
Benferhat, S., Cayrol, C., Dubois, D., Lang, J., Prade, H.: Inconsistency management and prioritized syntax-based entailment. In: Proceedings of the 13th International Joint Conference on Artificial Intelligence, Chambéry, France, August 28-September 3, pp. 640–647 (1993)
Benferhat, S., Dubois, D., Prade, H.: Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 2: The Prioritized Case 24, 473–511 (1998)
Bonzon, E., Lagasquie-Schiex, M.C., Lang, J.: Dependencies between players in boolean games. Int. J. Approx. Reasoning 50(6), 899–914 (2009)
Brewka, G.: Preferred subtheories: An extended logical framework for default reasoning. In: Proceedings of the 11th International Joint Conference on Artificial Intelligence, Detroit, MI, USA, pp. 1043–1048 (August 1989)
Brewka, G.: Reasoning about priorities in default logic. In: Proceedings of the 12th National Conference on Artificial Intelligence, Seattle, WA, USA, July 31-August 4, vol. 2, pp. 940–945 (1994)
Brewka, G.: A rank based description language for qualitative preferences. In: Proceedings of the 16th Eureopean Conference on Artificial Intelligence, ECAI 2004, including Prestigious Applicants of Intelligent Systems, PAIS 2004, Valencia, Spain, August 22-27, pp. 303–307 (2004)
Cayrol, C., Lagasquie-Schiex, M.: Non-monotonic syntax-based entailment: A classification of consequence relations. In: Froidevaux, C., Kohlas, J. (eds.) ECSQARU 1995. LNCS, vol. 946, pp. 107–114. Springer, Heidelberg (1995)
Cayrol, C., Lagasquie-Schiex, M., Schiex, T.: Nonmonotonic reasoning: From complexity to algorithms. Ann. Math. Artif. Intell. 22(3-4), 207–236 (1998)
Cayrol, C., Royer, V., Saurel, C.: Management of preferences in assumption-based reasoning. In: Valverde, L., Bouchon-Meunier, B., Yager, R.R. (eds.) IPMU 1992. LNCS, vol. 682, pp. 13–22. Springer, Heidelberg (1993)
Coste-Marquis, S., Lang, J., Liberatore, P., Marquis, P.: Expressive power and succinctness of propositional languages for preference representation. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Ninth International Conference (KR 2004), Whistler, Canada, June 2-5, pp. 203–212 (2004)
Coste-Marquis, S., Marquis, P.: On stratified belief base compilation. Ann. Math. Artif. Intell. 42(4), 399–442 (2004)
Delgrande, J.P., Dubois, D., Lang, J.: Iterated revision as prioritized merging. In: Proceedings of the Tenth International Conference on Principles of Knowledge Representation and Reasoning, Lake District of the United Kingdom, June 2-5, pp. 210–220 (2006)
Dubois, D., Fargier, H.: A unified framework for order-of-magnitude confidence relations. In: Proceedings of the 20th Conference in Uncertainty in Artificial Intelligence, UAI 2004, Banff, Canada, July 7-11, pp. 138–145 (2004)
Dubois, D., Fargier, H., Prade, H.: Refinements of the maximin approach to decision-making in a fuzzy environment. Fuzzy Sets and Systems (1996)
Dubois, D., Lang, J., Prade, H.: Inconsistency in Possibilistic Knowledge Bases: To Live with It or Not Live with It. In: Fuzzy logic for the management of uncertainty, pp. 335–351. John Wiley & Sons, Inc. (1992)
Everaere, P., Konieczny, S., Marquis, P.: Counting votes for aggregating judgments. In: Proceedings of the 13th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2014, pp. 1177–1184 (2014)
Fargier, H., Lang, J., Schiex, T.: Selecting preferred solutions in Fuzzy Constraint Satisfaction Problems. In: Proc. of the 1st European Congress on Fuzzy and Intelligent Technologies (1993)
Feldmann, R., Brewka, G., Wenzel, S.: Planning with prioritized goals. In: Proceedings of the Tenth International Conference on Principles of Knowledge Representation and Reasoning, Lake District of the United Kingdom, June 2-5, pp. 503–514 (2006)
Geffner, H.: Default Reasoning: Causal and Conditional Theories. MIT Press, Cambridge (1992)
Lang, J.: Logical preference representation and combinatorial vote. Ann. Math. Artif. Intell. 42(1-3), 37–71 (2004)
Lang, J., Pigozzi, G., Slavkovik, M., van der Torre, L.: Judgment aggregation rules based on minimization. In: TARK, pp. 238–246 (2011)
Lehmann, D.: Another perspective on default reasoning. Annals of Mathematics and Artificial Intelligence 15(1), 61–82 (1995)
Nebel, B.: Belief revision and default reasoning: Syntax-based approaches. In: Proceedings of the 2nd International Conference on Principles of Knowledge Representation and Reasoning (KR 1991), Cambridge, MA, USA, April 22-25, pp. 417–428 (1991)
Nehring, K., Pivato, M.: Majority rule in the absence of a majority. MPRA Paper 46721, University Library of Munich, Germany (May 2013), http://ideas.repec.org/p/pra//46721.html
Pearl, J.: System Z: A natural ordering of defaults with tractable applications to nonmonotonic reasoning. In: Proceedings of the 3rd Conference on Theoretical Aspects of Reasoning about Knowledge, Pacific Grove, CA, pp. 121–135 (March 1990)
Poole, D.: A logical framework for default reasoning. Artif. Intell. 36(1), 27–47 (1988)
Rescher, N.: Hypothetical Reasoning. Studies in Logic, North-Holland (1964)
Tideman, T.N.: Independence of clones as a criterion for voting rules. Social Choice and Welfare 4, 185–206 (1987)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Lang, J. (2015). Twenty-Five Years of Preferred Subtheories. In: Eiter, T., Strass, H., Truszczyński, M., Woltran, S. (eds) Advances in Knowledge Representation, Logic Programming, and Abstract Argumentation. Lecture Notes in Computer Science(), vol 9060. Springer, Cham. https://doi.org/10.1007/978-3-319-14726-0_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-14726-0_11
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-14725-3
Online ISBN: 978-3-319-14726-0
eBook Packages: Computer ScienceComputer Science (R0)