联言判断的五类表达形式适配高中数学必修一不同表述场景
The Five Categories of Expression Forms for Conjunctive Judgments and Their Adaptation to Different Descriptive Scenarios in Compulsory High School Mathematics Module 1
李宏 湖北省十堰市郧阳中学
Li Hong Yunyang High School, Shiyan City, Hubei Province
正确运用联言判断及推理的逻辑学基本原理（2）
Proper Use of Conjunctive Judgments and Reasoning
展开剩余92%联言判断的语言表达是其逻辑内涵的外在载体。
The linguistic expression of a conjunctive judgment serves as the external vehicle of its logical meaning.
2019 版必修一根据数学表述的需求（定义简洁、性质分层、特例说明、规则递进），灵活运用了并列复句、转折复句、递进复句、紧缩句、单句五种形式。
The 2019 edition of Compulsory Module I flexibly employs five forms---coordinate compound sentences, adversative compound sentences, progressive compound sentences, condensed sentences, and simple sentences---according to the needs of mathematical expression (such as concise definitions, layered properties, illustration of special cases, and progressive rules).
每种形式均对应明确的教材内容，且能清晰拆解出联言支与联结项。
Each form corresponds to specific textbook content and can be clearly decomposed into its conjuncts and connectives.
一、联言判断的五类表达形式的实例：
Examples of the Five Linguistic Forms of Conjunctive Judgment
1.并列复句实例：
Example of a Coordinate Complex Sentence:
空集是任何集合的子集，且是任何非空集合的真子集。
The empty set is a subset of every set and a proper subset of every non-empty set.
拆解：联言支①空集是任何集合的子集；②空集是任何非空集合的真子集；联结项为 “且”。
Decomposition:
Conjunct ① The empty set is a subset of every set;
Conjunct ② The empty set is a proper subset of every non-empty set;
Connectives: "and".
2.转折复句实例：
Example of an Adversative Compound Sentence:
虽然对数函数y=logax的单调性由底数a的取值决定，但是其定义域始终为(0,+∞)，且图象都过定点(1,0)。
Although the monotonicity of the logarithmic function y=logax is determined by the value of the base a, its domain is always (0,+∞), and its graph always passes through the fixed point (1,0).
拆解：联言支①单调性由a决定；②定义域为(0,+∞)；③图象过(1,0)；联结项为 “虽然… 但是…”“且”。
Decomposition:
Conjunct ①: Monotonicity is determined by a;
Conjunct ②: Domain is (0,+∞);
Conjunct ③: Graph passes through (1,0).
Connectives: "Although..., ..." and "and".
3.递进复句实例：
Example of a Progressive Complex Sentence:
函数的单调性不仅能直观刻画函数图象的上升或下降趋势，而且能定量描述自变量与函数值的变化关系。
The monotonicity of a function can not only intuitively depict the rising or falling trend of a function’s graph, but also quantitatively describe the relationship between the changes of the independent variable and the dependent variable.
拆解：联言支①单调性刻画图象趋势；②单调性定量描述变量变化关系；联结项为 “不仅… 而且…”。
Decomposition:
Conjunct ①: Monotonicity describes the trend of the graph;
Conjunct ②: Monotonicity provides a quantitative description of the relationship between variable changes;
Connective: "Not only... but also...".
4.紧缩句实例：
Example of a Condensed Sentence:
奇函数图象关于原点对称。
The graph of an odd function is symmetric about the origin.
拆解：补全联结项为 “一个函数是奇函数，且其图象关于原点对称”；
Decomposition: Supplement the connective term as "A function is an odd function, and its graph is symmetric about the origin";
联言支①函数是奇函数；②函数图象关于原点对称。
Conjunct ① A function is an odd function;
Conjunct ② The graph of the function is symmetric about the origin.
5.单句：核心用于概念定义，联结项完全省略
Simple Sentences: Primarily Used for Conceptual Definitions, with Connectives Entirely Omitted
通过定语、状语、宾语等单句成分承载联言支，是教材中核心概念定义的专属形式。
By embedding the conjuncts through sentence components such as attributives, adverbials, or objects, this form is exclusive to the definition of core concepts in textbooks.
既保证定义的简洁性，又能精准断定多本质特征同时存在。
It not only ensures the conciseness of the definition but also accurately asserts the simultaneous existence of multiple essential features.
实例：一般地，函数y=xα（α为常数）叫做幂函数。
Example: In general, a function of the form y=xα(where αis a constant) is called a power function.
拆解：联结项完全省略，补全后为 “一个函数的表达式为y=xα，且α为常数，该函数叫做幂函数”。
Breakdown:Connectives are entirely omitted. When fully expressed, it becomes: “A function whose expression is y=xαand whoseαis a constant is called a power function.”
联言支①表达式为y=xα；②α为常数。
Conjunct ①The expression is y=xα; ②αis a constant.
二、联言判断的语言表达形式主要包括：
Linguistic expressions of conjunctive judgments primarily include:
1.复句结构：
Compound sentences:
并列复句（例："他既勤奋又聪明"）
Coordinative clauses (e.g., "He is both diligent and smart")
转折复句（例："她贫穷却慷慨"）
Adversative clauses (e.g., "She is poor yet generous")
递进复句（例："他不仅道歉，还做出了赔偿"）
Progressive clauses (e.g., "Not only did he apologize, but he also compensated")
紧缩句（例："真实且公正"）
Contracted sentences (e.g., "Truthful and fair")
2.单句（例："风雨敲打着窗户"）
Simple sentences (e.g., "Rain and wind battered the window")
三、综上所述：
In Summary
联言判断的语言表达形式包括并列复句、转折复句、递进复句、紧缩句、单句。
The linguistic forms of conjunctive judgment include coordinate complex sentences, adversative complex sentences, progressive complex sentences, condensed sentences and simple sentences.
2019 版必修一根据表述目的（定义简洁、性质分层、特例说明、规律拓展）的不同，灵活选用对应形式。
The 2019 edition of Compulsory Mathematics Volume 1 flexibly adopts the corresponding forms according to different expressive purposes---concise definition, hierarchical presentation of properties, illustration of special cases and expansion of rules.
既保证数学表述的凝练性，又不违背 “断定多情况同时存在” 的逻辑核心。
This not only ensures the conciseness of mathematical expression, but also conforms to the logical core of "affirming that multiple states of affairs hold simultaneously".
各类形式均可清晰拆解出联言支，联结项或显化、或省略，逻辑关系明确。
Each form can be clearly decomposed into conjuncts, with connective terms either manifested or omitted, and the logical relations are explicit.
Explorer of Innovative Thinking
Author: Li Hong
Yunyang High School, Shiyan City, Hubei Province
January 27, 2026
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