Abstract
One of the important topics in the study of contraction inference relations is to establish the representation theorems for them. Various methods have been employed for giving representation of a broad class of contraction operations. However, there was not any canonical approach to dealing with the representation results for the contraction relations in the literature. Recently, in order to obtain the representation result for recovering contraction inference relations satisfying the condition weak conjunctive inclusion (wci), a notion of an image structure associated with the canonical epistemic state has been introduced. Based on the image structure, this paper establishes three representation results for recovering contraction inference relations which satisfy the conditions CL, CR1 and DR* respectively by the standard epistemic AGM states. A unique technique and uniform proofs to represent these contraction relations are adopted, which could overcome the core objection in previous description of contraction relations. The paper shows as well that the image structure and canonical epistemic states can be used not only to get the representation result for wci-recovering contraction relation, but also to provide semantic characterizations for a wide range of recovering contraction relations.
Similar content being viewed by others
References
Alchourrón C E, Gärdenfors P, Makinson D. On the logic of theory change: Partial meet contraction and revision functions. J. Symbolic Logic, 1985, 50(2): 510–530.
Fuhrmann A. Theory contraction through base contraction. J. Philosophical Logic, 1991, 20: 175–203.
Hansson S O. Theory contraction and base contraction unified. J. Symbolic Logic, 1993, 58: 602–625.
Nebel B. A knowledge level analysis of belief revision. In Proc. 1st Int. Conf. Principles of Knowledge Representation and Reasoning, Brachman R J (ed.), Morgan Kauffman, Los Altos, CA, 1989, pp.301–311.
Bochman A. A foundational theory of belief change. Artificial Intelligence, 1999, 108: 309–352.
Bochman A. Belief contraction as nonmonotonic inference. J. Symbolic Logic, 2000, 65(2): 605–626.
Bochman A. A foundationalist view of the AGM theory of belief change. Artificial Intelligence, 2000, 116: 237–263.
Zhaohui Zhu, Bin Li, Xi'an Xiao et al. A representation theorem for recovering contraction relations satisfying wci. Theoretical Computer Science, Jan. 2003, 290(1): 545–564.
Kraus S, Lehmann D, Magidor M. Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence, 1990, 44(1-2): 167–207.
Rott H. Belief contraction in the context of the general theory of rational choice. J. Symbolic Logic, 1993, 58(4): 1426–1450.
Freund M. Injective models and disjunctive relations. J. Logic and Computation, 1993, 3: 231–247.
Lehmann D, Magidor M. What does a conditional knowledge base entail? Artificial Intelligence, 1992, 55: 1–60.
Bezzazi H, Makinson D, Pino Pérez R. Beyond rational monotonicity: Some strong non-Horn rules for nonmonotonic inference relations. J. Logic and Computation, 1997, 7: 605–631.
Zhaohui Zhu, Shifu Chen, Wujia Zhu. Valuation structure. J. Symbolic Logic, 2002, 67(1): 1–23.
R Pino Pérez, C Uzcátegui. On representation theorems for nonmonotonic inference relation. J. Symbolic Logic, 2000, 65(3): 1321–1337.
Author information
Authors and Affiliations
Corresponding author
Additional information
This research was supported by the National Natural Science Foundation of China (Grant Nos.60175017 and 60496327) and NSF of Jiangsu Province (Grant No.BK2001046).
Rights and permissions
About this article
Cite this article
Hou, P. Some Representation Theorems for Recovering Contraction Relations. J Comput Sci Technol 20, 536–541 (2005). https://doi.org/10.1007/s11390-005-0536-9
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s11390-005-0536-9