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AGM Theory and Artificial Intelligence

  • Raúl CarnotaEmail author
  • Ricardo Rodríguez
Chapter
  • 650 Downloads
Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 21)

Abstract

A very influential work on belief change is based on the seminal paper “On the Logic of Theory Change: Partial Meet Contractions and Revision Functions”. In this paper Alchourron, Gärdenfors, and Makinson investigate the properties that such a method should have in order to be intuitively appealing. The result was a set of postulates (named AGM postulates after the initials of the authors) that every belief change operator should satisfy. The “AGM Theory” had a major influence in most subsequent works on belief change. In special, the constructive approach given there was adopted in Artificial Intelligence (AI) as the (almost) universal model for the specification of the updates of Knowledge Bases as it usually involves a new belief that may be inconsistent with the old ones. From that moment, the references to the original paper within the field of AI have increased drastically. In this chapter we intend to explain why AGM receive such swift acceptance from the AI community. We will show that the AGM theory came out at a critical time for AI. In particular, the question of how to actualize the knowledge bases in the face of inputs that are possible inconsistent with the previous corpus, was an unresolved, problematic issue. This is why, when AGM appears, it combines with various attempts under development that synchronize perfectly with them, as is the case with the pioneering work we will be discussing in this chapter. The high level of abstraction of the new approach was what a lot of researchers in AI were seeking.

This chapter also contains a description of the genesis of AGM theory, a historical analysis of the circumstances in which the theory was introduced to AI, and a qualitative and quantitative evaluation of the impact of the AGM theory in AI research.

Keywords

Knowledge Level Belief Revision Belief Base Belief Change Conditional Sentence 
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.

Notes

Acknowledgments

We would not be able even to attempt to reconstruct the history of the introduction of the AGM Theory in Artificial Intelligence without invaluable contributions of many of the principle actors of those years’ long, extensive and effervescent discussions. All of them approached our inquiry with enthusiasm and made true efforts to honor us with their emotive memories.

Therefore we want to thank Cristina Bicchieri, Horacio Arló Costa, Alex Borgida, Mukesh Dalal, Norman Foo, Peter Gärdenfors, Joseph Halpern, Gilbert Harman, David Israel, Hirofumi Katsumo, Hector Levesque, Bernhard Nebel, Hans Rott, Ken Satoh, Karl Schlechta for accepting to respond our questions and being our partners this time.

We are very grateful to our friend Eduardo Fermé for his sharp observations that helped us to revise the original Spanish draft of our work.

Also, we are indebted to our colleague and friend José Alvarez who helped us to translate to English our first draft. In addition, during this process, he offered us a lot of helpful and interesting discussions on different parts of this chapter.

We own a very special gratitude to Gladys Palau, Eugenio Bulygin, David Makinson and Antonio Martino who committed themselves in a very personal way to the reconstruction of the history, patiently accepting our repeated inquiries and generously sharing their reminiscences of Carlos Alchourrón.

Thanks all of them to accompany us to honor the memory of Carlos Alchourrón whose disciples and friends we consider ourselves to be.

References

  1. Alchourrón, C. 1986. Conditionality and the representation of legal norms. In Automated analysis of legal texts, eds. A.A. Martino and F. Socci Natale, 175–186. Amsterdam: North Holland.Google Scholar
  2. Alchourrón, C., and D. Makinson. 1981. Hierarchies of regulations and their logic. In New studies in deontic logic, ed. R. Hilpinen, 125–148. Dordrecht: Reidel.Google Scholar
  3. Alchourrón, C., and D. Makinson. 1982. On the logic of theory change: Contraction functions and their associated Revision functions. Theoria. A Swedish Journal of Philosophy XLVIII:14–37.Google Scholar
  4. Alchourrón, C., and D. Makinson. 1985. On the logic of theory change: safe contraction. Studia Logica 44:405–422.CrossRefGoogle Scholar
  5. Alchourrón, C., and D. Makinson. 1986. Maps between some different kinds contraction function: the finite case. Studia Logica 45:187–198.CrossRefGoogle Scholar
  6. Alchourrón, C., P. Gärdenfors, and D. Makinson. 1985. On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic 50(2):118–139.Google Scholar
  7. Bicchieri, Cristina. 1988a. Strategic behavior and counterfactuals. Synthese 76:135–169CrossRefGoogle Scholar
  8. Bicchieri, Cristina. 1988b. Common knowledge and backward induction: A solution to the paradox. In Proceedings of the second conference on theoretical aspects of reasoning about knowledge (2nd TARK), 381–393. California, CA.Google Scholar
  9. Borgida, A. 1985. Language features for flexible handling of exceptions in information systems. ACM Transactions on Database Systems 10:565–603.Google Scholar
  10. Dalal, Mukesh. 1988. Investigations into a theory of knowledge base revision. Preliminary report. In Proceedings of the conference of the American association for artificial intelligence. August 21–26, 475–479. Sant Paul, MN.Google Scholar
  11. Darwiche, Adnan, and Peral Judea. 1997. On the logic of iterated belief revision. Artificial Intelligence 89:1–29.CrossRefGoogle Scholar
  12. Doyle, Jon. 1979. A truth maintenance system. Artificial Intelligence 12(2):231–272.Google Scholar
  13. Doyle, Jon., and London, Philip. 1980. A selected descriptor-indexed bibliography to the literature on belief revision. ACM SIGART Bulletin 71:7–22.Google Scholar
  14. Fagin, Ronald, Ullman, Jeffrey, and Vardi, Moshe. 1983. On the semantics of updates in databases. In Proceedings of the Second ACM-SIGACT-SIGMOD.SIGART Symposium on Principles of Database Systems, 352–365. Atlanta, GA.Google Scholar
  15. Fagin, R., G.M. Kuper, J.D. Ullman, and M.Y. Vardi. 1986. Updating logical databases. In Advances in computing research, eds. P. Kanellakis and F.P. Preparata, vol. 3, 1–18. London: JAI Press.Google Scholar
  16. Friedman, N., and J. Halpern. 1999. Belief revision: A critique. Journal of Logic, Language and Information, 8:401–420.Google Scholar
  17. Furhmann, A., and M. Morreau. 1990. Preface of “The Logic of Theory Change”. In Lecture Notes in Artificial Intelligence. Berlin: Springer.Google Scholar
  18. Gärdenfors, Peter. 1979. Conditionals and changes of belief. In The logic and epistemology of scientific change, eds. I. Niiniluoto and R. Tuomela, 381–404. Amsterdam: North Holland.Google Scholar
  19. Gärdenfors, Peter. 1980. A pragmatic approach to explanations. Philosophy of Science 47:404–423.CrossRefGoogle Scholar
  20. Gärdenfors, Peter. 1981. An epistemic approach to conditionals. American Philosophical Quarterly 18:203–211.Google Scholar
  21. Gärdenfors, Peter. 1982. Rules for rational changes of belief. In Philosophical essays dedicated to Lennart Aqvist on his fiftieth birthday, ed. T. Pauli, 88–101. Department of de Philosophy, Universidad de Uppsala.Google Scholar
  22. Gärdenfors, Peter. 1986. Belief revision and the Ramsey test for conditionals. The Philosophical Review 95:81–93.CrossRefGoogle Scholar
  23. Gärdenfors, P. 1988. Knowledge in flux, 67. Cambridge, MA: MIT.Google Scholar
  24. Gärdenfors, P., and D. Makinson. 1988. Revision of knowledge systems using epistemic entrenchment. In Proceedings of the Second Conference TARK, 83–95. California, CA.Google Scholar
  25. Gärdenfors, P., and D. Makinson. 1991. Relation between the logic of theory change and non monotonic logic. In Lecture Notes in Artificial Intelligence vol. 465, eds. A. Furman and M. Morreau, 185–205. Berlin: Springer.Google Scholar
  26. Graubard Stephen, R. 1988. The artificial intelligence debate: False starts and real foundations. Cambridge, MA: MIT PressGoogle Scholar
  27. Gärdenfors, Peter, and Rott. Hans. 1992. Belief revision. 11. Lundt University Cognitive Studies.Google Scholar
  28. Halpern, J. 1986. Reasoning about knowledge: An overview. In Proceedings of the First Conference TARK. Monterey, CA.Google Scholar
  29. Harper, W. 1977. Rational conceptual change. In Philosophy of science association, 462–494. University of Chicago.Google Scholar
  30. Katsuno, H., and A. Mendelzon. 1989. A unified view of propositional knowledge base updates. In Proceedings of the 11th IJCAI, 1413–1419. Detroit, MI: Morgan KauffmanGoogle Scholar
  31. Kelly, K., O. Schulk, and V. Hendricks. 1997. Reliable belief revision. In logic and scientific methods, 179–208. New York, NY: Kluwer.Google Scholar
  32. Levesque, H.J. 1984. Foundations of a functional approach to knowledge representation. Artificial Intelligence 23:155–212.CrossRefGoogle Scholar
  33. Levesque, H.J. 1986. Knowledge representation and reasoning. Annual Review of Computer Science 1:255–287.Google Scholar
  34. Levesque H.J. 1988. Logic and the complexity of reasoning. Journal of Philosophical Logic 17:355–389.CrossRefGoogle Scholar
  35. Levi, I. 1977. Subjunctives, dispositions and chances. Synthese 34:423–455.CrossRefGoogle Scholar
  36. Levi, I. 1980. The enterprise of knowledge. Cambridge, MA: MIT.Google Scholar
  37. Makinson, David. 1989. General theory of cumulative inference. In Non-monotonic reasoning, eds. Michael Reinfrank, Johan de Kleer, Matthew L. Ginsberg, and Erik Sandewall, 2nd International Workshop, Grassau, FRG, June 13–15, 1988, Proceedings. Lecture Notes in Computer Science 346. Berlin: Springer.Google Scholar
  38. Makinson, David. 1996. In Memoriam, eds. Carlos Eduardo Alchourrón. Nordic Journal of Philosophical Logic 1(1):3–10Google Scholar
  39. Makinson, David, and Kourousias George. 2006. Respecting relevance in belief change. Análisis Filosófico XXVI(1). Buenos Aires, Mayo, 53–61Google Scholar
  40. McCarthy, J. 1977. Epistemological problems of artificial intelligence. Proceedings of the Fifth International Joint Conference on Artificial Intelligence, 1038–1044. Cambridge, MA: M.I.TGoogle Scholar
  41. McCarthy, J., 1980. Circumscription. A form of non-monotonic reasoning. Artificial Intelligence 13:41–72Google Scholar
  42. McCarthy, J., and P. J. Hayes. 1969. Some philosophical problems from the standpoint of artificial intelligence. In Machine intelligence, eds. B. Meltzer, and D. Michie, 4:463–502. Edinburgh: Edinburgh University Press.Google Scholar
  43. Nebel, Bernhard. 1989. A knowledge level analysis of belief revision. In Principles of knowledge representation and reasoning, eds. R.J. Brachman, H.J. Levesque, and R. Reiter, 301–311. San Francisco, CA: Morgan Kaufmann.Google Scholar
  44. Nebel, Bernhard. 1992. Syntax-based approaches to belief revision. In Belief revision, ed. P. Gärdenfors. Cambridge Tracts in Theoretical Computer Science 29, New York, NY: Cambridge University Press.Google Scholar
  45. Newell, Alan. 1981. The knowledge level. The AI Magazine 2(2):1–20.Google Scholar
  46. Rao, A.S., and N. Foo. 1989. Minimal change and maximal coherence – A basis for belief revision and reasoning about actions. In Proceedings of the Eleventh International Joint Conference on Artificial Intelligence, 966–971. San Mateo: Morgan Kaufmann.Google Scholar
  47. Reiter, Ray. 1980. A logic for default reasoning. Artificial Intelligence 13:81–132Google Scholar
  48. Rott, Hans. 1989. Conditionals and theory change: Revision, expansions and additions. Synthese 81:91–113.CrossRefGoogle Scholar
  49. Satoh, Ken. 1988. Non monotonic reasoning by minimal belief revision. In Proceedings of the International Conference on Fifth Generation Computer Systems, 455–462, Tokio, Japan.Google Scholar
  50. Schlechta, Karl. 1989. Some results on belief revision. In Proceedings of the workshop on the logic of theory change, Konstanz.Google Scholar
  51. Vardi, M. 1988. Preface for the edition of the Proceedings of the second conference TARK (Theoretical Aspects of Reasoning about Knowledge), California, USA.Google Scholar
  52. Weber, A. 1986. Updating propositional formulas. In Proceedings of the Expert Database Systems Conference, Charleston, SC.Google Scholar
  53. Winslett, M. 1986. Is belief revision harder than you thought? In AAAI86 proceedings, 421–427 August 11–15, Philadelphia, PA.Google Scholar
  54. Winslett, M. 1988. A model-based approach to updating databases with incomplete information. ACM Transactions on Database Systems 13(2):167–196.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Universidad Nacional de Tres de FebreroBuenos AiresArgentina
  2. 2.Departamento de Computación de la Facultad de Ciencias Exactas y NaturalesUniversidad de Buenos AiresBuenos AiresArgentina

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