Skip to main content
Log in

On the equivalence of upward and downward inheritance reasoners

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

In this paper, we analyze systematically the downward (property flow) and the upward (individual flow) views of inheritance for different categories of inheritance networks. We observe that both these views assign the same meaning to tree-structured hierarchies, and explain the divergence in the interpretation of more general networks in terms of their expressive power. This simple analysis sheds light on the inherent nature of nonmonotonic inheritance and can form the basis for the design of efficient algorithms for certain classes of queries. In addition, we describe the notion of preferential inheritance to specify additional conflict resolution information that can be integrated smoothly with the upward view of inheritance.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. H. Geffner, Default reasoning: Causal and conditional theories, Ph.D. Dissertation, University of California at Los Angeles (1989).

  2. J. Horty, R. Thomason and D. Touretzky, A skeptical theory of inheritance in nonmonotonic semantic networks, Artificial Intelligence 42(1990)311–348.

    Google Scholar 

  3. J. Horty, A credulous theory of mixed inheritance, in:Inheritance Hierarchies in Knowledge Representation and Programming Languages, eds. M. Lenzerini et al. (Wiley, 1991).

  4. B. Meyer,Object-Oriented Software Construction (Prentice-Hall, 1988).

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

    Google Scholar 

  6. K. Thirunarayan, An analysis of property-flow view vs. individual-flow view of inheritance,Proc. 6th Int. Symp. on Methodologies for Intelligent Systems (1991) pp. 256–265.

  7. T. Krishnaprasad, M. Kifer and D.S. Warren, On the declarative semantics of inheritance networks,Proc. 11th Int. Joint Conf. on Artificial Intelligence (1989) pp. 1093–1098.

  8. T. Krishnaprasad, The semantics of inheritance networks, Ph.D. Dissertation, State University of New York at Stony Brook (1989).

    Google Scholar 

  9. H. Przymusinska and M. Gelfond, Inheritance hierarchies and autoepistemic logic, Technical Report, Computer Science Department, University of Texas at El Paso (1989).

    Google Scholar 

  10. E. Sandewall, Nonmonotonic inference rules for multiple inheritance with exceptions, Proc. IEEE 74(1986)1345–1353.

    Google Scholar 

  11. B. Selman and H.J. Levesque, The tractability of path-based inheritance,Proc. 11th Int. Joint Conf. on Artificial Intelligence (1989) pp. 1140–1145.

  12. M. Stefik and D.G. Bobrow, Object-oriented programming: Themes and variations, AI Magazine (1986) 40–62.

  13. L.A. Stein, Resolving ambiguity in nonmonotonic inheritance hierarchies, Artificial Intelligence 55(1992)259–310.

    Google Scholar 

  14. R. Thomason and J. Horty, Logics for inheritance theory,Non-Monotonic Reasoning, eds. M. Reinfrank et al. (Springer, 1989).

  15. D. Touretzky,The Mathematics of Inheritance Systems (Morgan Kaufmann, Los Altos, 1986).

    Google Scholar 

  16. D. Touretzky, J. Horty and R. Thomason, A clash of intuitions: The current state of nonmonotonic multiple inheritance systems,Proc. 10th Int. Joint Conf. on Artificial Intelligence (1987) pp. 476–482.

Download references

Author information

Authors and Affiliations

Authors

Additional information

This research was supported in part by NSF grant IRI-9009587.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Thirunarayan, K. On the equivalence of upward and downward inheritance reasoners. Ann Math Artif Intell 15, 239–256 (1995). https://doi.org/10.1007/BF01534457

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01534457

Keywords

Navigation