Knowledge Reasoning Involving Four Types of Syllogisms

TL;DR

This paper explores the validity and reasoning processes of complex generalized syllogisms involving quantifiers like 'most' and 'all', providing formal proofs and deductions to support language information processing.

Contribution

It introduces formal knowledge representations for generalized syllogisms and proves the validity of a specific syllogism, extending understanding of syllogistic reasoning in language.

Findings

Proved the validity of generalized syllogism AMI-1

Deduced multiple valid classical and modal syllogisms from AMI-1

Provided a framework for judging discourse reasoning validity

Abstract

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.