基于四值语义的缺省逻辑

基于公式变换，给出一组缺省理论的变换方法，将命题语言L中的缺省理论变换到对应的命题语言L^-＋中，保证了所得到的缺省理论的所有扩张均不平凡，并通过一种弱变换可同时保证缺省扩张的存在性．为缺省理论定义了各种四值模型，使得缺省逻辑具有非单调超协调推理能力，并证明了L^-＋中的缺省扩张与L中缺省理论的四值模型之间具有一一对应关系．四值模型描述了公式变换的语义，基于四值语义的缺省推理通过缺省理论的变换技术能在标准的缺省逻辑中实现．

Default Logic Based on Four Valued Semantics

By the formula transformations, a set of transformations for a default theory is provided. The default theory in a propositional language L is transformed into the corresponding language L~+, and thus all the extensions of the transformed default theory are non-trivial. A weak transformation of default theory is also given to ensure the existence of the default extensions. The various four-valued models are defined for default theories such that the default logic has the ability of nonmonotonic paraconsistent reasoning. It is proved that there is a one-to-one relationship between the extensions of L~+ and the four-valued models of default theory of L. The four-valued models describe semantics for the formula transformations. The default reasoning based on four valued semantics can be computed in the context of standard default logic by the transformation technique of default theories.