描述例外的基数模态逻辑系统  

A Cardinal Modal Logic for Describing Exceptions

作　　者：罗昊轩 郭佳宏 Haoxuan Luo;Jiahong Guo

机构地区：[1]北京师范大学哲学学院

出　　处：《逻辑学研究》2024年第5期21-38,共18页Studies in Logic

基　　金：国家社会科学基金重大项目“大数据背景下人工智能及其逻辑的哲学反思”(19ZDA041)。

摘　　要：本文关注的问题是如何对允许例外情况存在的几乎必然命题进行形式化。在日常交流和科学研究中,很多普遍形式表述的命题都存在着例外情况,只是例外情况有时可以被忽略。为了区分含有不同程度例外情况的普遍性陈述,本文借助基数的概念,构造了基数模态算子,用来描述例外存在但可以忽略的情况。基于该算子,我们称一个命题是几乎必然的,当且仅当不存在足够多的例外情况不满足该命题。接着本文提出了基数模态逻辑系统,证明了该系统的可数模型性,并运用过滤与模型的复制构造了该系统的典范模型,以此说明系统的完全性。由此表明,本文提出的描述例外的基数模态逻辑系统实现了表达力扩充与对自然语言更精确刻画的一种相对平衡。In this paper,the question we are concerned with is how to formalise almost necessary propositions to which describing the existence of exceptions in reality.In daily communication and scientific research,many propositions formulated in a universal form have exceptions,except that the exceptions can sometimes be ignored.In order to distinguish between universal statements containing different degrees of exceptions,we construct the basic modal operator with the help of the notion of cardinality,which is used to describe the cases where exceptions exist but can be ignored.Based on this operator,we claim that a proposition is almost necessary if and only if there do not exist a sufficient number of exceptions that do not satisfy the proposition.The article then presents a system of cardinal modal logic,proves the countable model property of the system,and uses the replication of the model to construct an exemplary model of the system as a way of illustrating the completeness of the system.It has been thus shown that the cardinal modal logic system for describing exceptions proposed in the paper achieves a relative balance between expressive power expansion and a more accurate portrayal of natural language.

关 键 词：基数 几乎必然命题 基数模态逻辑 典范模型 可数模型性 

分 类 号：B81[哲学宗教—逻辑学]