扩展的逻辑程序系统及其语义理论

THE SEMANTIC FRAMEWORK OF AN EXTENDED LOGIC PROGRAMMING SYSTEM

将逻辑程序系统由一阶逻辑中解放出来是复杂对象推理所迫切需要的.本文提出扩展的逻辑程序语言HILOG并建立其语义理论,扩充了逻辑程序系统的形式语义.HILOG为一带类型语言.通过建立诸如p-包含及装配/拆卸等代数概念,本文扩充了逻辑满足及模型比较等概念,证明了一HILOG程序具有一最小模型闭包及标准(装配形式)最小模型的唯一性,提出了模型的p-相交定理及扩充的最小模型极小不动点性质.一阶逻辑程序语义在上述各方面恰为HILOG语义之特殊情况,二者语义上的联系提供了将HILOG程序映射到一阶系统的可能性.

The formal framework of a strongly typed, extended LP system HILOG is proposed. Through the introduction of appropriate mathematical concepts such as partial containment, packing and unpacking, the notions of the satisfaction, the existence of a minimal model closure, the uniqueness of a standard (packed) minimal model for a HILOG program, the model p-intersection theorem, and the extended least fixpoint characteristics of the HILOG minimal model, have been developed. Therefore, HILOG has a generalized canonical framework and covers the first order LP as its special case. The semantic link between them provides the mapping of HILOG programs to FOL programs. The development of HILOG is significant for representing structured knowledge, handling type hierarchies, supporting multilevel reasoning and enhance the usability of LP.