An Algebraic Characterization of Equivalent Preferential Models

Journal of Symbolic Logic 72 (3):803 - 833 (2007)
  Copy   BIBTEX


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



    Upload a copy of this work     Papers currently archived: 76,479

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Valuation structure.Zhaohui Zhu, Zhenghua Pan, Shifu Chen & Wujia Zhu - 2002 - Journal of Symbolic Logic 67 (1):1-23.
Algebraic semantics for deductive systems.W. J. Blok & J. Rebagliato - 2003 - Studia Logica 74 (1-2):153 - 180.
A brief introduction to algebraic set theory.Steve Awodey - 2008 - Bulletin of Symbolic Logic 14 (3):281-298.
Completeness and incompleteness for plausibility logic.Karl Schlechta - 1996 - Journal of Logic, Language and Information 5 (2):177-192.


Added to PP

13 (#768,873)

6 months
1 (#455,463)

Historical graph of downloads
How can I increase my downloads?

References found in this work

No references found.

Add more references