Skip to main content

Abstract

Inheritance is a powerful concept that has been extensively used in the context of data modeling in databases, programming in object-oriented paradigm, and knowledge representation in artificial intelligence. Because of the close relationship between inheritance and deduction, logic is one of the obvious candidates for a declarative framework for inheritance. However, inheritance has resisted many serious attempts at a satisfactory logical rendition. In this paper, we shall survey various proposals in the literature for formalizations of inheritance and classify them based on the kind of inheritance they capture (structural or behavioral, monotonic or nonmonotonic, value inheritance or definition inheritance), and also based on their expressive power. We also classify the proposals from the perspective of the underlying logical framework they are based on (e.g., proof theory or model theory, etc). We conclude the paper with a list of what, from our perspective, are the most significant problems requiring further research in this field. Our focus in this paper will be primarily on the database and knowledge representation fronts.

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. Bacchus, F. A modest, but semantically well-founded, inheritance reasoner. In Proceedings of the Eleventh IJCAI, pp. 1104–1109, 1989.

    Google Scholar 

  2. Belnap, N. A useful four-valued logic. Modern uses of multi-valued logic, pp. 8–37, 1977.

    Google Scholar 

  3. Bugliesi, M. and Jamil, M. A stable model semantics for behavioral inheritance in deductive object oriented languages. In G. Gottlob and M. Vardi, editors, Proceedings of the 5th International Conference on Database Theory (ICDT), pp. 222–237, Prague, Czech Republic, 1995. Springer-Verlag.

    Google Scholar 

  4. Brass, S. and Lipeck, W. Semantics of inheritance in logical object specifications. In Proceedings of the Intl. Conf. on Deductive and Object-Oriented Databases, pp. 411–430, 1991.

    Google Scholar 

  5. Brewka, G. Preferred Subtheories: An Extended Logical Framework for Default Reasoning. In Proceedings of the Eleventh IJCAI, pp. 1043–1048, 1989.

    Google Scholar 

  6. Bugliesi, M. A declarative view of inheritance in logic programming. In K. Apt, editor, Proc. Joint Int. Conference and Symposium on Logic Programming, pp. 113–130. The MIT Press, 1992.

    Google Scholar 

  7. Cardelli, L. and Wegner, P. On understanding types, data abstraction, and polymorphism. Computing Surveys, 17(4):471–522, 1985.

    Article  Google Scholar 

  8. Dalai, M. and Gangopadhyay, D. OOLP: A translation approach to object-oriented logic programming. In Proceedings of the First DOOD Conference, pp. 593–606, 1990.

    Google Scholar 

  9. Dobbie, G. and Topor, R. A model for inheritance and overriding in deductive object-oriented systems. Sixteen Australian Computer Science Conference, January 1988.

    Google Scholar 

  10. Dobbie, G. and Topor, R. A model for sets and multiple inheritance in deductive object-oriented systems. In Proc. 3rd Intl. DOOD Conf., pp. 473–488, 1993.

    Google Scholar 

  11. Etherington, D. and Reiter, R. On inheritance hierarchies with exceptions. In Proceedings of the Second National Conference on Artificial Intelligence, pp. 104–108, 1983.

    Google Scholar 

  12. Fahlman, S.E. NETL: A System for Representing and Using Real-World Knowledge. The MIT Press, Cambridge, MA, 1979.

    MATH  Google Scholar 

  13. Fitting, M. The family of stable models. Journal of Logic Programming, 17, November 1993.

    Google Scholar 

  14. Geffner, H. Default Reasoning: Causal and Conditional Theories. PhD thesis, University of California at Los Angeles, 1989.

    Google Scholar 

  15. Ginsberg, M.L. A local formalization of inheritance: preliminary report. Unpublished Manuscript, Stanford University, 1988.

    Google Scholar 

  16. Geffner, H. and Pearl, J. A framework for reasoning with defaults. In Proceedings of Society for Exact Philosophy Conference, 1988.

    Google Scholar 

  17. Horty, J. Some direct theories of nonmonotonic inheritance. Handbook of Logic in Artifical Intelligence and Logic Programming. Oxford University Press, 1993.

    Google Scholar 

  18. Horty, J., Thomason, R., and Touretzky, D. A skeptical theory of inheritance in nonmonotonic semantic networks. In Proceedings of the Sixth AAAI, pp. 358–363, 1987.

    Google Scholar 

  19. Horty, J., Thomason, R., and Touretzky, D. Mixing strict and defeasible inheritance. In Proceedings of the Seventh AAAI, pp. 427–432, 1988.

    Google Scholar 

  20. Jamil, H.M. and Lakshmanan, L.V.S. A declarative semantics for behavioral inheritance and conflict resolution. In Proceedings of the 12th International Logic Programming Symposium, pp. 130–144, 1995.

    Google Scholar 

  21. Jamil, H.M. and Lakshmanan, L.V.S. A declarative semantics for behavioral inheritance and conflict resolution. Journal of Logic Programming (to appear), 1997.

    Google Scholar 

  22. Kraus, S., Lehmann, D., and Magidor, M. Nonmonotonic Reasoning, Preferential Models and Cumulative Logics. Artificial Intelligence, 44:167–207, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  23. Kifer, M., Lausen, G., and Wu, J. Logical Foundations for Object-Oriented and Frame-Based Languages. Journal of the Association of Computing Machinery, 42(4):741–843, July 1995.

    Article  MathSciNet  MATH  Google Scholar 

  24. Kaci, H. and Nasr, A. A logic programming language with built-in inheritance. Journal of Logic Programming, 3:182–215, 1986.

    Google Scholar 

  25. Kaci, H. and Podelski, A. Towards a Meaning of LIFE. Tech. report, Digital Paris Research Labs, 1991.

    Google Scholar 

  26. Laenens, E. and Vermeir, D. A fixpoint semantics for ordered logic. Journal of Logic and Computation, 1(2):159–185, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  27. McCarthy, J. Applications of circumscription to formalizing common-sense knowledge. Artificial Intelligence, 28:89–116, 1986.

    Article  MathSciNet  Google Scholar 

  28. McCabe, F.G. Logic and Objects. Prentice Hall International, London, 1992.

    MATH  Google Scholar 

  29. Monteiro, L. and Porto, A. A transformational view of inheritance in logic programming. In Proc. 7th Int. Conference on Logic Programming, pp. 481–494, 1990.

    Google Scholar 

  30. Monteiro, L. and Porto, A. Syntactic and semantic inheritance in logic programming. In Workshop on Declarative Programming. Springer-Verlag, 1991.

    Google Scholar 

  31. Makinson, D. and Schlechta, K. Floating conclusions and zombie paths: two deep difficulties in the “directly skeptical” approach to defeasible inheritance nets. Artificial Intelligence, 48:199–209, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  32. Neufeld, E. Notes on “A clash of intuitions”. Artificial Intelligence, 48:225–240, 1991.

    Article  Google Scholar 

  33. Przymusinska, H. and Gelfond, M. Formalization of inheritance reasoning in autoepistemic logic. Fundamenta Informaticae, 13(4):403–444, 1990.

    MathSciNet  MATH  Google Scholar 

  34. Sandewall, E. Nonmonotonic inference rules for multiple inheritance with exceptions. In Proceedings of the IEEE, volume 74:10, pp. 1345–1353, 1986.

    Article  Google Scholar 

  35. Selman, B. and Levesque, H.J. The tractability of path-based inheritance. In Proceedings of the Eleventh IJCAI, pp. 1140–1145, 1989.

    Google Scholar 

  36. Stein, L.A. Resolving ambiguity in nonmonotonic inheritance hierarchies. Artificial Intelligence, 55:259–310, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  37. Taivalsaari, A. On the Notion of Inheritance. ACM Computing Surveys, 28(3):438–479, 1996.

    Article  Google Scholar 

  38. Thomason, R. and Horty, J. Logics for inheritance theory. In Nonmonotonic Reasoning. Springer-Verlag, 1989.

    Google Scholar 

  39. Thirunarayan, K. Local theories of inheritance. International Journal of Intelligent Systems, 10(7):617–645, 1995.

    Article  Google Scholar 

  40. Thirunarayan, K. On the Equivalence of Upward and Downward Inheritance Reasoners. Annals of Mathematics and Artificial Intelligence, 15(2):239–256, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  41. Thomason, R., Horty, J., and Touretzky, D. A calculus for inheritance in monotonic semantic nets. In Proceedings of the Second ISMIS, pp. 280–287, 1987.

    Google Scholar 

  42. Touretzky, D., Horty, J., and Thomason, R. A clash of intuitions: the current state of nonmonotonic multiple inheritance systems. In Proceedings of the Tenth IJCAI, pp. 476–482, 1987.

    Google Scholar 

  43. Thirunarayan, K. and Kifer, M. A theory of nonmonotonic inheritance based on annotated logic. Artificial Intelligence, 60:23–50, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  44. Touretzky, D. The Mathematics of Inheritance Systems. Morgan Kaufmann, Los Altos, 1986.

    MATH  Google Scholar 

  45. Touretzky, D., Thomason, R., and Horty, J. A skeptic’s menagerie: conflictors, preemptors, reinstaters, and zombies in nonmonotonic inheritance. In Proceedings of the Twelfth IJCAI-91, pp. 478–483, 1991.

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer Science+Business Media New York

About this chapter

Cite this chapter

Lakshmanan, L.V., Thirunarayan, K. (1998). Declarative Frameworks for Inheritance. In: Chomicki, J., Saake, G. (eds) Logics for Databases and Information Systems. The Springer International Series in Engineering and Computer Science, vol 436. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5643-5_11

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-5643-5_11

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7582-1

  • Online ISBN: 978-1-4615-5643-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics