Journal of Symbolic Logic

An algebraic characterization of equivalent preferential models

Rong Zhang and Zhaohui Zhu

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Abstract

Preferential model 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.

Article information

Source
J. Symbolic Logic, Volume 72, Issue 3 (2007), 803-833.

Dates
First available in Project Euclid: 2 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1191333843

Digital Object Identifier
doi:10.2178/jsl/1191333843

Mathematical Reviews number (MathSciNet)
MR2354902

Zentralblatt MATH identifier
1203.03043

Keywords
nonmonotonic logic preferential model model-theoretical properties

Citation

Zhu, Zhaohui; Zhang, Rong. An algebraic characterization of equivalent preferential models. J. Symbolic Logic 72 (2007), no. 3, 803--833. doi:10.2178/jsl/1191333843. https://projecteuclid.org/euclid.jsl/1191333843


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