科研之友
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摘要
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 Delta(center dot) and mu(center dot) over preferential models are introduced and explored respectively. Together with other two existent operators rho(center dot) and Pi(D)(center dot), we introduce an operator delta(D)(center dot). Then the isomorphism theorem is obtained in terms of delta(D)(center dot), which asserts that for any two preferential models M(1) and M(2), they generate the same preferential inference if and only if delta(D)(M(1)) and delta(D)(M(2)) are isomorphic. Based on delta(D)(center dot), we also get an alternative modeltheoretical characterization of the well-known postulate Weaken Disjunctire Rationality. Moreover, in the finite language framework, we show that Delta(mu(center dot)) is competent for the task of eliminating redundancy, and provide a representation result for k-relations.
