This paper studies the validity and discourse reasoning of non-trivial generalized syllogisms involving the quantifiers in Square{most} and Square{all} from the perspective of knowledge reasoning. Firstly, this paper presents knowledge representations for these syllogisms and formally proves the validity of generalized syllogism AMI-1. Subsequently, 19 non-trivial generalized syllogisms, 22 non-trivial valid generalized modal syllogisms, 8 valid classical syllogisms, and 24 valid classical modal syllogisms are respectively deduced from the valid generalized syllogism AMI-1 on the basis of deductive reasoning. Additionally, this paper discusses how to judge the validity of discourse reasoning nested by the above four types of syllogisms, which have four types of figures and different forms. In conclusion, such formal deductions not only provide a theoretical foundation for English language information processing, but also provide methodological insights for studying other syllogistic systems.

翻译：本文从知识推理的视角，研究了涉及Square{most}与Square{all}量词的非平凡广义三段论的有效性与语篇推理。首先，本文提出了这些三段论的知识表示，并形式化证明了广义三段论AMI-1的有效性。随后，基于演绎推理，从有效的广义三段论AMI-1出发，分别推导出19个非平凡广义三段论、22个非平凡有效的广义模态三段论、8个有效的经典三段论以及24个有效的经典模态三段论。此外，本文探讨了如何判断由上述四种类型三段论嵌套构成的语篇推理的有效性，这些三段论具有四种格与不同形式。综上所述，此类形式化推导不仅为英语语言信息处理提供了理论基础，也为研究其他三段论系统提供了方法论启示。