| 走向模型论的模态逻辑 | |
| 马明辉 ; Minghui Ma | |
| 2010-06-07 ; 2010-06-07 | |
| 关键词 | 模型论 一阶逻辑 模态逻辑 分级模态词 B815.1 |
| 其他题名 | Toward Model-Theoretic Modal Logics |
| 中文摘要 | 增加特定的基数量词,扩张一阶语言,就可以导致实质性地增强语言的表达能力,这样许多超出一阶逻辑范围的数学概念就能得到处理。由于在模型的层次上基本模态逻辑可以看作一阶逻辑的互模拟不变片断,显然它不能处理这些数学概念。因此,增加说明后继状态类上基数概念的模态词,原则上我们就能以模态的方式处理所有基数。我们把讨论各种模型论逻辑的方式转移到模态方面。; By adding certain cardinality quantifiers,we can extend first order logic so as to obtain an actually more powerful language.Thus many mathematical concepts beyond the capability of first-order logic can be coped with.Mostowski proposed cardinality quantifiers in 1957,and new fields of logic concerning generalized quantifiers have been explored from then on.In the so called model theory,techniques and methods in model theory of first order logic are widely used.Logics can be investigated in an way.One excellent example is Lindstr(?)m's characterization theorem which says that certain logic can be definitely determined by some certain model-theoretic properties.Various results on relations between logics are obtained. On the other hand,the relationship between modal logic and classical logics has been greatly promoted by some authors,especially Johan van Benthem.Because of the notion of bisimulation,modal model theory has been developed.Since the basic modal logic may be treated as the bisimulation invariant fragment of first-order logic,those mathematical concepts beyond first order logic obviously cannot be treated within it. Actually,basic modal logic can be embedded into two variable fragment of first order logic.This is a hint of a direction of investigation;to study fragments of first order logic which posses nice properties. My program is to combine the two directions of investigation.Graded modal logic, which is explored by some Italian logicians in 1980s,provides a good paradigm.In this sort of logic,graded modalities(?)_n which says that there are at least n successors are added in to basic modal logic.Generalized quantifiers in principle can be treated modally by adding new modalities expressing cardinalities on the class of certain successor state. Modes of exploring model-theoretic logics can be transferred to modal logics.This paper shows some topics in this direction. |
| 语种 | 中文 ; 中文 |
| 内容类型 | 期刊论文 |
| 源URL | [http://hdl.handle.net/123456789/44666]  |
| 专题 | 清华大学 |
| 推荐引用方式 GB/T 7714 | 马明辉,Minghui Ma. 走向模型论的模态逻辑[J],2010, 2010. |
| APA | 马明辉,&Minghui Ma.(2010).走向模型论的模态逻辑.. |
| MLA | 马明辉,et al."走向模型论的模态逻辑".(2010). |
| 个性服务 |
| 查看访问统计 |
| 相关权益政策 |
| 暂无数据 |
| 收藏/分享 |
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。
修改评论