计算机科学中的一些逻辑理论的推理性质研究

DEDUCTION PROPERTY OF SOME LOGICS APPLIED TO COMPUTER SCIENCE

由于一阶谓词逻辑的基本特征是具有可靠性、完全性，在推广一阶谓词逻辑表达能力及扩充其推理能力时，可以定义一些具有可靠性、完全性的逻辑，对此，在分析逻辑理论特征的基础上，给出一些逻辑的推理系统之间相似性的实质，证明这些逻辑在实质上并不能扩充一阶谓词逻辑的推理能力，并指出非单调推理中的缺省推理及限定推理所采用的技术是扩充时必需的．

The soundness and completeness are the characterization properties of first order predicate logic, which are explored in many logics extending the classical logic. Based on the analysis of these logical properties, this paper reveals the essence leading to the similarity among the deduction systems of many logics, proves that many logics used can not extend the deduction power of first order predicate logic, and points out that the technique involved in default logic and circumscription in nonmonotonic reasoning should be employed when doing extension.