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An algebraic characterization of equivalent preferential models

Published online by Cambridge University Press:  12 March 2014

Zhaohui Zhu  and
Rong Zhang
Zhaohui Zhu
Affiliation:
Department of Computer Science, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016., P. R. China Shanghai Key Lab of Intelligent Information Processing, Fudan University, Shanghai, 200433, P.R. China. E-mail: [email protected]
Rong Zhang
Affiliation:
State Key Lab of Novel Software Technology, Nanjing University, Nanjing, 210093, P. R. China Shanghai Key Lab of Intelligent Information Processing, Fudan University, Shanghai, 200433, P.R. China. E-mail: [email protected]
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Abstract

Preferential models is one of the important semantical structures in nonmonotonic logic. This paper aims to establish an isomorphism theorem for preferential models, which gives us a purely algebraic characterization of the equivalence of preferential models. To this end, we present the notions of local similarity and local simulation. Based on these notions, two operators Δ(•) and μ(•) over preferential models are introduced and explored respectively. Together with other two existent operators ρ(•) and ΠD(•), we introduce an operator ∂D(•). Then the isomorphism theorem is obtained in terms of ∂D(•), which asserts that for any two preferential models M1 and M2, they generate the same preferential inference if and only if ∂D(M1) and ∂D(M2) are isomorphic. Based on ∂D(•), we also get an alternative model-theoretical characterization of the well-known postulate Weaken Disjunctive Rationality. Moreover, in the finite language framework, we show that Δ(μ(•)) is competent for the task of eliminating redundancy, and provide a representation result for k-relations.

Keywords

nonmonotonic logicpreferential modelmodel-theoretical properties
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 3 , September 2007 , pp. 803 - 833
Copyright
Copyright © Association for Symbolic Logic 2007

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