Skip to main content

Logics for Belief Base Updating

  • Chapter
  • First Online:
Belief Change

Part of the book series: Handbook of Defeasible Reasoning and Uncertainty Management Systems ((HAND,volume 3))

Abstract

A database is a device to store and retrieve information. In the terminology of Levesque [Levesque, 1984], a database comes equipped with a querying function ASK and an update function TELL. The query ASK (light-on) means that the database is asked whether it follows from the data contained in it that the light in question is on. The answer is basically ‘yes’ or ‘no’. (There might be more cooperative answers such as a variable substitution à la PROLOG.) In the simplest case light-on ollows from the database just if light-on explicitly appears in it, but in the case of more expressive systems such as logical databases the answering mechanism resorts to deduction.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C. Alchourrón, P. Gärdenfors and D. Makinson. On the logic of theory change: Partial meet contraction and revision functions. J. of Symbolic Logic, 50: 510–530, 1985.

    Article  MathSciNet  Google Scholar 

  2. A. R. Anderson and N. D. Belnap. Entailment, volume 1. Princeton University Press, 1975.

    Google Scholar 

  3. H. Arló Costa and S. Shapiro. Maps between nonmonotonic and conditional logics. In B. Nebel, C. Rich and W. Swartout, editors, Proc. 4th Int. Conf. on Knowledge Representation and Reasoning (KR′92), pages 553–564. Morgan Kaufmann Publishers, 1992.

    Google Scholar 

  4. S. Benferhat, C. Cayrol, D. Dubois, J. Lang and H. Prade. Inconsistency management and prioritized syntax-based entailment. In R. Bajcsy, editor, Proc. 13th Int. Joint Conf. on Artificial Intelligence (IJCAI′93), pages 640–645. Morgan Kaufmann Publishers, 1993.

    Google Scholar 

  5. C. Boutilier. Conditional logics of normality as modal systems. In Proc. 10th Nat. Conf. on Artificial Intelligence (AAAI′90), pages 594–599. AAAI Press/MIT Press, 1990.

    Google Scholar 

  6. J. P. Burgess. Quick completeness proofs for some logics of conditionals. Notre Dame J. of Formal Logic, 22: 76–84, 1981.

    Article  MathSciNet  Google Scholar 

  7. J. P. Burgess. Basic tense logic. In D. M. Gabbay and F. Günthner [1984], pages 89–134.

    Google Scholar 

  8. B. Chellas. Basic conditional logics. J. of Philosophical Logic, 4: 133–153, 1975.

    Article  MathSciNet  Google Scholar 

  9. B. Chellas. Modal logic: An introduction. Cambridge University Press, 1980.

    Google Scholar 

  10. T. Chou and M.-A. Winslett. Immortal: A model-based belief revision system. In J. Allen, R. Fikes, and E. Sandewall, editors, Proc. 3rd Int. Conf. on Knowledge Representation and Reasoning (KR′91), pages 99–110. Morgan Kaufmann Publishers, 1991.

    Google Scholar 

  11. T. Chou and M.-A. Winslett. A model-based belief revision system. J. of Automated Reasoning, 12: 157–208, 1994.

    Article  MathSciNet  Google Scholar 

  12. G. Crocco and L. Farinas del Cerro. Structure, consequence relation and logic. In D. M. Gabbay, editor, What is a logical system?, number 4 in Studies in Logic and Computation, pages 239–259. Oxford University Press, 1994.

    Google Scholar 

  13. G. Crocco. Fondements logiques du raisonnement contextuel. PhD thesis, Paul Sabatier University, Toulouse, 1993.

    Google Scholar 

  14. M. Dalal. Investigations into a theory of knowledge base revision: preliminary report. In Proc. 7th Conf. on Artificial Intelligence (AAAI′88), pages 475–479, 1988.

    Google Scholar 

  15. G. de Giacomo. Eliminating ‘converse’ from Converse PDL. J. of Logic, Language and Information, 5: 193–208, 1996.

    Article  MathSciNet  Google Scholar 

  16. A. Del Val and Y. Shoham. A unified view of belief revision and update. J. of Logic and Computation, 4(5):797–810, 1994.

    Article  MathSciNet  Google Scholar 

  17. A. Del Val. Computing knowledge base updates. In Proc. 4th Int. Conf. on Knowledge Representation and Reasoning (KR′92), pages 740–750, 1992.

    Google Scholar 

  18. A. Del Val. Non monotonie reasoning and belief revision: syntactic, semantic, foundational, and coherence approaches. J. of Applied Non-classical Logics (JANCL), 7(2):213–240, 1997.

    Article  Google Scholar 

  19. D. Dubois and H. Prade. Possibility TheoryAn Approach to Computerized Processing of Uncertainty. Plenum Press, New York, 1988. (with the collaboration of H. Farreny, R. Martin-Clouaire, C. Testemale).

    Google Scholar 

  20. T. Eiter and G. Gottlob. On the complexity of propositional knowledge base revision, updates, and counterfactuals. Artificial Intelligence J., 57: 227–270, 1992.

    Article  MathSciNet  Google Scholar 

  21. T. Eiter, G. Gottlob and Y. Gurevich. Curb your theory! a circumscriptive approach for inclusive interpretation of disjunctive information. In R. Bajcsy, editor, Proc. 13th Int. Joint Conf. on Artificial Intelligence (IJCAI′93), pages 640–645. Morgan Kaufmann Publishers, 1993.

    Google Scholar 

  22. L. Farinas del Cerro and A. Herzig. An automated modal logic for elementary changes. In Ph. Smets, A. Mamdani, D. Dubois, and H. Prade, editors, Non-Standard Logics for Automated Reasoning, pages 63–79. Academic Press, 1988.

    Google Scholar 

  23. L. Farinas del Cerro and A. Herzig. A conditional logic for updating in the possible models approach. In B. Nebel and L. Dreschler-Fischer, editors, Proc. 18th German Conf. on Artificial Intelligence (KI′94), number 861 in LNAI, pages 237–247. Springer-Verlag, sep 1994.

    Google Scholar 

  24. L. Farinas del Cerro and A. Herzig. Revisions, updates, and interference. In A. Fuhrmann and H. Rott, editors, Logic and Information, pages 189–207. DeGruyter Publishers, Berlin, 1995.

    Google Scholar 

  25. L. Farinas del Cerro and A. Herzig. All other things being equal: on a notion of inertia in conditional logic. In E. Ejerhed and S. Lindstrm, editors, Logic, Action and Cognition — Selection of papers of the Umea colloquium on dynamic approaches in Logic, Language and Information (UmLLI-93), Trends in Logic, pages 137–148. Kluwer Academic Publishers, 1997.

    Google Scholar 

  26. K. D. Forbus. Introducing actions into qualitative simulation. In N. S. Sridharan, editor, Proc. 11th Int. Joint Conf. on Artificial Intelligence (IJCAI′89), pages 1273–1278. Morgan Kaufmann Publishers, 1989.

    Google Scholar 

  27. D. M. Gabbay and F. Giinthner, editors. Handbook of Philosophical Logic, volume II. D. Reidel, Dordrecht, 1984.

    Google Scholar 

  28. D. M. Gabbay, C. J. Hogger, and J. A. Robinson, editors. Handbook of Logic in Artificial Intelligence and Logic Programming, volume 4. Oxford University Press, 1995.

    Google Scholar 

  29. D. M. Gabbay. Theoretical foundations for non-monotonic reasoning in expert systems. In Krysztof R. Apt, editor, Logics and Models of Concurrent Systems, pages 439–457. Springer-Verlag, 1985.

    Google Scholar 

  30. P. Gärdenfors and D. Makinson. Revisions of knowledge systems using epistemic entrenchment. In Proc. 2nd Conf. on Theoretical Aspects of Reasoning about Knowledge, pages 83–95, 1988.

    Google Scholar 

  31. P. Gärdenfors and H. Rott. Belief revision. In Gabbay et al. [1995], pages 35–132.

    Google Scholar 

  32. P. Gärdenfors. Conditionals and changes of belief. In I. Niiniluoto and R. Tuomela, editors, The Logic and Epistemology of Scientific Change, volume 30, pages 381–404. Acta Philosophica Fennica, 1978.

    Google Scholar 

  33. P. Gärdenfors. Knowledge in Flux: Modeling the Dynamics of Epistemic States. MIT Press, 1988.

    Google Scholar 

  34. G. Grahne and A. O. Mendelzon. Updates and subjunctive queries. Information and Computation, 116: 241–252, 1995.

    Article  MathSciNet  Google Scholar 

  35. G. Grahne. Updates and counterfactuals. In J. Allen, R. Fikes, and E. Sandewall, editors, Proc. 3rd Int. Conf. on Knowledge Representation and Reasoning (KR′91), pages 269–276. Morgan Kaufmann Publishers, 1991. extended version to appear in the J. of Logic and Computation.

    Google Scholar 

  36. A. Grove. Two modellings for theory change. J. of Philosophical Logic, 17: 157–170, 1988.

    Article  MathSciNet  Google Scholar 

  37. S. O. Hansson. A test battery for rational database updating. Artificial Intelligence J., 82: 341–352, 1996.

    Article  MathSciNet  Google Scholar 

  38. D. Harel. Dynamic logic. In Gabbay and Günthner [1984], pages 497–604.

    Google Scholar 

  39. A. Herzig. The PMA revisited. In L. C. Aiello and S. Shapiro, editors, Proc. Int. Conf. on Knowledge Representation and Reasoning (KR ′96), pages 40–50. Morgan Kaufmann Publishers, November 1996.

    Google Scholar 

  40. H. Katsuno and A. O. Mendelzon. A unified view of propositional knowledge base updates. In Proc. 11th Int. Joint Conf. on Artificial Intelligence (IJCAI′89), pages 1413–1419, 1989.

    Google Scholar 

  41. H. Katsuno and A. O. Mendelzon. Propositional knowledge base revision and minimal change. Artificial Intelligence 7., 52: 263–294, 1991.

    Article  MathSciNet  Google Scholar 

  42. H. Katsuno and A. O. Mendelzon. On the difference between updating a knowledge base and revising it. In P. Gärdenfors, editor, Belief revision, pages 183–203. Cambridge University Press, 1992. (preliminary version in Allen, J.A., Fikes, R., and Sandewall, E., eds., Principles of Knowledge Representation and Reasoning: Proc. 2nd Int. Conf., pages 387-394. Morgan Kaufmann Publishers, 1991).

    Google Scholar 

  43. H. Katsuno and K. Satoh. A unified view of consequence relation, belief revision, and conditional logic. In G. Crocco, L. Farinas del Cerro, and A. Herzig, editors, Conditionals: from philosophy to computer science, number 5 in Studies in Logic and Computation, pages 33–65. Oxford University Press, 1995. (preliminary version in: Proc. Int. Joint Conf. on Artificial Intelligence (UCAI′91), Morgan Kaufmann Publishers, 1991).

    Google Scholar 

  44. A. M. Keller and M. Winslett. On the use of an extended relational model to handle changing incomplete information. In IEEE Transaction on Software Engineering, volume SE-11: 7, pages 620–633, 1985.

    Article  Google Scholar 

  45. M. Kracht and F. Wolter. Properties of independently axiomatizable bimodal logics. 7. of Symbolic Logic, 56: 1469–1485, 1991.

    Article  MathSciNet  Google Scholar 

  46. P. Lamarre. S4 as the conditional logic of nonmonotonicity. In J. Allen, R. Fikes, and E. Sandewall, editors, Proc. 3rd Int. Conf. on Knowledge Representation and Reasoning (KR′91), pages 269–276. Morgan Kaufmann Publishers, 1991.

    Google Scholar 

  47. H. Levesque. Foundations of a functional approach to knowledge representation. Artificial Intelligence J., 23: 155–212, 1984.

    Article  Google Scholar 

  48. D. Lewis. Counterfactuals. Basil Black well, Oxford, 1973.

    MATH  Google Scholar 

  49. V. Lifschitz. Frames in the space of situations. Artificial Intelligence J., 46: 365–376, 1986.

    Article  MathSciNet  Google Scholar 

  50. D. Makinson. Five faces of minimality. Studia Logica, 52: 339–379, 1993.

    Article  MathSciNet  Google Scholar 

  51. D. Makinson. General patterns in nonmonotonic reasoning. In D. M. Gabbay, C. J. Hogger, and J. A. Robinson, editors, Handbook of Logic in Artificial Intelligence and Logic Programming, volume 3, pages 35–110. Oxford University Press, 1994.

    Google Scholar 

  52. W. Nejdl. The P-systems: A systematic classification of logics of nonmonotonicity. In Proc. 11th Nat. Conf. on Artificial Intelligence (AAAI′91), pages 366–372. AAAI Press/MIT Press, 1991.

    Google Scholar 

  53. D. Nute. Topics in conditional logic. D. Reidel, Dordrecht, 1980.

    Google Scholar 

  54. D. Nute. Conditional logic. In Gabbay and Günthner [1984], pages 387–439.

    Google Scholar 

  55. M. Ryan and P.-Y. Schobbens. Intertranslating counterfactuals and updates. J. of Logic, Language and Information, 6(2): 123–146, 1997. (preliminary version in: W. Wahlster (ed.), Proc. ECAF96.).

    Google Scholar 

  56. Léa Sombé. A glance at revision and updating in knowledge bases. International J. of Intelligent Systems, 9(1): 1–27, January 1994. (P. Besnard, L.Cholvy, M.O. Cordier, D. Dubois, L. Farinas del Cerro, C. Froidevaux, F. Levy, Y. Moinard, H. Prade, C. Schwind, P. Siegel).

    Article  MathSciNet  Google Scholar 

  57. R. Stalnaker. A theory of conditionals. Studies in Logical Theory, American Philosphical Quarterly (Monograph Series, No. 2). Blackwell, Oxford, 1968. (reprinted in E. Sosa, ed., Causation and Conditionals. Oxford University Press, 1975; reprinted in W. L. Harper, R. Stalnaker and G. Pearce, eds., Ifs. Reidel, Dordrecht, 1981; reprinted in W. L. Harper and B. Skyrms, eds., Causation in Decision, Belief Change and Statistics, Vol.2. Reidel, Dordrecht, 1988, pp 105-134; reprinted in F. Jackson, ed., Conditionals. Oxford University Press, Oxford Readings in Philosophy, 1991).

    Google Scholar 

  58. R. Stalnaker. What is a nonmonotonic consequencerelation? In (Informal) Working Notes of the 4th Int. Workshop on Nonmonotonic Reasoning, Plymouth, Vermont, 1992.

    Google Scholar 

  59. J. van Benthem. Temporal logic. In Gabbay et al. [1995], pages 241–350.

    Google Scholar 

  60. M.-A. Winslett. Reasoning about action using a possible models approach. In Proc. 7th Conf. on Artificial Intelligence (AAAI′88), pages 89–93, St. Paul, 1988.

    Google Scholar 

  61. M.-A. Winslett. Updating Logical Databases. Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1990.

    Google Scholar 

  62. M.-A. Winslett. Updating logical databases. In Gabbay et al. [1995], pages 133–174.

    Google Scholar 

  63. F. Wolter. A counterexample in tense logic. Notre Dame J. of Formal Logic, 37(2), 1997. (special issue on combining logics).

    Google Scholar 

  64. Y. Zhang and N. Y. Foo. Updating knowledge bases with disjunctive information. In Proc. AAAl′96, pages 562–568. AAAI/MIT Press, 1996.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Herzig, A. (1998). Logics for Belief Base Updating. In: Dubois, D., Prade, H. (eds) Belief Change. Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5054-5_5

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-5054-5_5

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6123-0

  • Online ISBN: 978-94-011-5054-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics