Skip to main content

Infinitary default logic for specification of nonmonotonic reasoning

  • Default Logics
  • Conference paper
  • First Online:
Logics in Artificial Intelligence (JELIA 1996)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1126))

Included in the following conference series:

  • 133 Accesses

Abstract

In this paper we study constructions leading to the formation of belief sets by agents. We focus on the situation when possible belief sets are built incrementally in stages. We call an infinite sequence of theories that represents such a process a reasoning trace. A set of reasoning traces describing all possible reasoning scenarios for the agent is called a reasoning frame. Default logic by Reiter is not powerful enough to represent reasoning frames. In the paper we introduce a generalization of default logic of Reiter by allowing infinite sets of justifications. We call this formalism infinitary default logic. In the main result of the paper we show that every reasoning frame can be represented by an infinitary default theory. A similar representability result for antichains of theories (belief frames) is also presented.

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

Access this chapter

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. J. Engelfriet, H. Herre and J. Treur. Nonmonotonic Belief State Frames and Reasoning Frames (extended abstract). In C. Froidevaux, J. Kohlas (eds), Proceedings of the European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty, Lecture Notes in Artificial Intelligence, Vol. 946, Springer-Verlag, 1995, pp. 189–196.

    Google Scholar 

  2. J. Engelfriet, H. Herre and J. Treur. Nonmonotonic Reasoning with Multiple Belief Sets. In D.M. Gabbay, H.J. Ohlbach (eds), Proceedings of the International Conference on Formal and Applied Practical Reasoning, Lecture Notes in Artificial Intelligence, Vol. 1085, Springer-Verlag,1996, pp. 331–344.

    Google Scholar 

  3. J. Engelfriet and J. Treur. Specification of Nonmonotonic Reasoning. In D.M. Gabbay, H.J. Ohlbach (eds), Proceedings of the International Conference on Formal and Applied Practical Reasoning, Lecture Notes in Artificial Intelligence, Vol. 1085, Springer-Verlag, 1996, pp. 111–125.

    Google Scholar 

  4. A. Ferry. Enriched nonmonotonic rule system. Master of Science Dissertation, University of Kentucky, 1991.

    Google Scholar 

  5. W. Marek and M. Truszczyński. Nonmonotonic logics; context-dependent reasoning. Berlin: Springer-Verlag, 1993.

    Google Scholar 

  6. W. Marek, J. Treur, and M. Truszczyňski. Representability by default theories. In Proceedings of the Fourth International Symposium on Artificial Intelligence and Mathematics, 1996.

    Google Scholar 

  7. R. Reiter. A logic for default reasoning. Artificial Intelligence, 13:81–132, 1980.

    Article  Google Scholar 

  8. T. Schaub. On constrained default theories. In B. Neumann (ed.), Proceedings of the European Conference on Artificial Intelligence, 1992, pp. 304–308

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

José Jülio Alferes Luís Moniz Pereira Ewa Orlowska

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Engelfriet, J., Marek, V.W., Treur, J., Truszczyński, M. (1996). Infinitary default logic for specification of nonmonotonic reasoning. In: Alferes, J.J., Pereira, L.M., Orlowska, E. (eds) Logics in Artificial Intelligence. JELIA 1996. Lecture Notes in Computer Science, vol 1126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61630-6_15

Download citation

  • DOI: https://doi.org/10.1007/3-540-61630-6_15

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61630-6

  • Online ISBN: 978-3-540-70643-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics