arXivDaily arXiv每日学术速递 周一至周五更新
arXiv cs/0207091cs.LO
收藏

一种用于逻辑程序设计和非单调推理的几乎经典逻辑

An Almost Classical Logic for Logic Programming and Nonmonotonic Reasoning

François Bry

摘要:

介绍了一种称为N^4的一阶逻辑的模型理论。N^4并不像经典逻辑那样消除双重否定,而是减少了四重否定。N^4非常接近经典逻辑:N^4有两个真值; N^4中的蕴涵是实质性的,就像在经典逻辑中一样;否定分布在N^4中的复合公式中,就像在经典逻辑中一样。结果表明,正规逻辑程序的语义可以方便地用N^4形式化:经典逻辑Herbrand解释可以直接推广到N^4;正逻辑程序的经典最小Herbrand模型与其唯一的最小N^4 Herbrand模型一致;正规逻辑程序的稳定模型与其所谓的完全最小N^4 Herbrand模型一致.

英文摘要:

The model theory of a first-order logic called N^4 is introduced. N^4 does not eliminate double negations, as classical logic does, but instead reduces fourfold negations. N^4 is very close to classical logic: N^4 has two truth values; implications in N^4 are material, like in classical logic; and negation distributes over compound formulas in N^4 as it does in classical logic. Results suggest that the semantics of normal logic programs is conveniently formalized in N^4: Classical logic Herbrand interpretations generalize straightforwardly to N^4; the classical minimal Herbrand model of a positive logic program coincides with its unique minimal N^4 Herbrand model; the stable models of a normal logic program and its so-called complete minimal N^4 Herbrand models coincide.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑