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.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
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.
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.
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.
A. Ferry. Enriched nonmonotonic rule system. Master of Science Dissertation, University of Kentucky, 1991.
W. Marek and M. Truszczyński. Nonmonotonic logics; context-dependent reasoning. Berlin: Springer-Verlag, 1993.
W. Marek, J. Treur, and M. Truszczyňski. Representability by default theories. In Proceedings of the Fourth International Symposium on Artificial Intelligence and Mathematics, 1996.
R. Reiter. A logic for default reasoning. Artificial Intelligence, 13:81–132, 1980.
T. Schaub. On constrained default theories. In B. Neumann (ed.), Proceedings of the European Conference on Artificial Intelligence, 1992, pp. 304–308
Author information
Authors and Affiliations
Editor information
Rights 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