Skip to main content
Springer Nature Link
Log in

Declarative program theory with implicit implication

  • Knowledge Representation I
  • Conference paper
  • First Online:
PRICAI'96: Topics in Artificial Intelligence (PRICAI 1996)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1114))

Included in the following conference series:

Abstract

In order to provide a general framework for deductive object-oriented representation systems, Akama's declarative program theory is extended under the assumptions that there exists implicit implication among elements of an interpretation domain and that this implicit implication can be represented by a preorder on the domain. Under the consequent constraint that every interpretation must conform to the implicit implication, an appropriate model-theoretic semantics as well as its corresponding fixpoint semantics for declarative programs is described. Based on Köstler et. al.'s foundation of fixpoint with subsumption, it is shown that if the implicit-implication relation is further assumed to be a partial order, then the meaning of a program can be determined more efficiently by the application of an immediate-consequence operator which involves only the reduced representations, basically consisting only of their maximal elements, of subsets of the interpretation domain.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. K. Akama. Declarative Semantics of Logic Programs on Parameterized Representation Systems. Technical report, Hokkaido University, Sapporo, Japan, 1990.

    Google Scholar 

  2. K. Akama. Generalized Logic Programs on Specialization Systems and SLDA Resolution. Technical report, Hokkaido University, Sapporo, Japan, 1990.

    Google Scholar 

  3. K. Akama. Declarative Semantics of Logic Programs on Parameterized Representation Systems. Advances in Software Science and Technology, 5:45–63, 1993. A revised version of [1].

    Google Scholar 

  4. K. Akama. Sufficient Conditions of Inference Rules for Declarative Programs. Technical report, Hokkaido University, Sapporo, Japan, 1994.

    Google Scholar 

  5. K. Akama. Logical Formalization of Problems Using Declarative Programs. Technical report, Hokkaido University, Sapporo, Japan, 1995.

    Google Scholar 

  6. P. M. Dung. On the Acceptability of Arguments and Its Fundamental Role in Nonmonotonic Reasoning, Logic Programming and N-Person Games. Artificial Intelligence, 77(2):321–357, September 1995.

    Google Scholar 

  7. B. C. Ghosh and V. Wuwongse. Declarative Semantics of Conceptual Graph Programs. In Proceedings of the Second Workshop on Peirce held in conjunction with the First International Conference on Conceptual Structures (ICCS'93), Quebec City, Canada, August 1993.

    Google Scholar 

  8. B. C. Ghosh and V. Wuwongse. Inference Systems for Conceptual Graph Programs. In W. M. Tepfenhart, J. P. Dick, and J. F. Sowa, editors, Proceedings of the Second International Conference on Conceptual Structures (ICCS'94), volume 835 of Lecture Notes in Artificial Intelligence, pages 214–229, College Park, Maryland, USA, August 1994. Springer-Verlag.

    Google Scholar 

  9. B. C. Ghosh and V. Wuwongse. A Direct Proof Procedure for Definite Conceptual Graph Programs. In G. Ellis, R. Levinson, W. Rich, and J. F. Sowa, editors, Proceedings of the Third International Conference on Conceptual Structures (ICCS'95), volume 954 of Lecture Notes in Artificial Intelligence, pages 158–172, Santa Cruz, CA, USA, August 1995. Springer-Verlag.

    Google Scholar 

  10. B. C. Ghosh and V. Wuwongse. Conceptual Graph Programs and Their Declarative Semantics. IEICE Transactions on Information and Systems, E78-D(9):1208–1217, September 1995.

    Google Scholar 

  11. M. Kifer, G. Lausen, and J. Wu. Logical Foundations of Object-Oriented and Frame-Based Languages. Journal of the Association for Computing Machinery, pages 741–843, July 1995.

    Google Scholar 

  12. G. Köstler, W. Kießling, H. Thöne, and U. Güntzer. The Differential Fixpoint Operator with Subsumption. In S. Ceri, K. Tanaka, and S. Tsur, editors, Proceedings of the Third International Conference on Deductive and Object-Oriented Databases (DOOD'93), volume 760 of Lecture Notes in Computer Science, pages 35–48, Phoenix, Arizona, USA, December 1993. Springer-Verlag.

    Google Scholar 

  13. G. Köstler, W. Kießling, H. Thöne, and U. Güntzer. Fixpoint Iteration with Subsumption in Deductive Databases. Journal of Intelligent Information Systems, 4(2):123–148, March 1995. A revised and extended version of [12].

    Google Scholar 

  14. V. Wuwongse and E. Nantajeewarawat. Declarative Program Theory with Interpretation-Dependent Implicit Implication. Technical report, Computer Science Program, School of Advanced Technologies, Asian Institute of Technology, Bangkok 10501, Thailand, September 1995.

    Google Scholar 

  15. V. Wuwongse and E. Nantajeewarawat. Declarative Program Theory with Implicit Implication. Technical report, Computer Science Program, School of Advanced Technologies, Asian Institute of Technology, Bangkok 10501, Thailand, April 1996.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science and Information Management Program School of Advanced Technologies, Asian Institute of Technology, GPO Box 2754, 10501, Bangkok, Thailand

    Vilas Wuwongse & Ekawit Nantajeewarawat

Authors
  1. Vilas Wuwongse
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ekawit Nantajeewarawat
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Norman Foo Randy Goebel

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wuwongse, V., Nantajeewarawat, E. (1996). Declarative program theory with implicit implication. In: Foo, N., Goebel, R. (eds) PRICAI'96: Topics in Artificial Intelligence. PRICAI 1996. Lecture Notes in Computer Science, vol 1114. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61532-6_9

Download citation

  • DOI: https://doi.org/10.1007/3-540-61532-6_9

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61532-3

  • Online ISBN: 978-3-540-68729-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics