辩护逻辑研究

发布时间：2018-02-27 23:10

本文关键词： 辩护逻辑证明逻辑逻辑全能公共知识格蒂尔问题　出处：《南京大学》2015年硕士论文　论文类型：学位论文

【摘要】：辩护逻辑是用于认知推理的逻辑系统群。以在传统逻辑形式化进程中缺失的辩护算子作为研究对象,辩护逻辑吸收了数学证明论和主流的认识论观点,在古典命题逻辑的基础上建立发展。证明逻辑LP是整个辩护逻辑家族谱系中最早的成员。它的建立源于阿尔捷莫夫把口F解释成Proof(t,F)这样一个关系函数的想法,这替换了哥德尔将口F解释成Provable (F),并将其等同于xProof(x, F)的观点。他认为这种把隐式证明项转换成显式证明项的做法不仅实现了S4系统对LP的适当嵌入,合理地解决了S4对第二不完全性定理的违反问题,而且也为S4提供了期望已久的可证性语义学。之后,阿尔捷莫夫将证明逻辑应用于认知论中,并在此基础上建立发展了其他的辩护逻辑系统。但阿尔捷莫夫并没有把证明逻辑作为基本辩护逻辑系统,而是把只包含LP中应用和总计公理的系统J作为标准辩护逻辑系统。在J中,t：F不再解释成t是F的证明,而是解释成t是F的一个辩护。而t是证明多项式,它由辩护常量和辩护变量通过一元算子证明检验“!”以及二元算子应用“·”和结合“+”组成。当t仅是辩护常量,F是J中的逻辑公理时,包含所有t：F形式的公式集合称为J系统的常量参数。在该系统中,所有的推导都是在给定常量参数下进行的推导,因为它指定了辩护公理的辩护项。J系统的语义模型是克里普克模型加上可接受证据函数ε(t,F),后者是辩护多项式和公式集到可能世界的映射。相对于这样的语义模型,J是可靠的和完全的。并且,通过将逻辑意识、充分规则、正自省规则和负自省规则对应的认知公理添加于J系统中,得到的其他的辩护逻辑系统J4、J45、JT、JT4、JT45和JD45也是可靠的和完全的。由于把口F转换成t：F这样的特殊结构,辩护逻辑系统避免了传统模态知识逻辑所具有的逻辑全能问题,这让我们可以更安全地通过辩护逻辑来扩充自身的知识。在刻画公共知识方面,基于证明逻辑LP与常见的多主体知识逻辑系统Tn、S4n和S5n之上建立的得到辩护的知识系统TnJ、S4Jn和S5nJ,不仅能够让我们清楚得到知识背后的原因,其自身系统中所带有的常规削减法也令公共知识的获得过程之刻画变得合理可行,弥补了传统知识逻辑在理论和实践方面的缺陷。而一阶辩护逻辑对格蒂尔问题的分析,不但揭示了该问题的本质,更展现了它自身强大的表达刻画能力。辩护逻辑是认知逻辑中的新兴课题,它还有很大的发展空间,比如量化辩护逻辑的发展,S4LP、LPP等辩护逻辑系统的建立完善等。因而对辩护逻辑的研究具有重要的学科意义和时代意义。本文在对相关经典文献解读的基础上,系统梳理了辩护逻辑的发展过程,详细说明了辩护逻辑的主要内容,适当评价了辩护逻辑在哲学应用方面的价值。
[Abstract]:Defence logic is a group of logic systems used in cognitive reasoning. Taking the defense operator missing in the formalization process of traditional logic as the research object, the defense logic absorbs the mathematical proof theory and the mainstream epistemological viewpoint. On the basis of classical propositional logic, the proof logic LP is the earliest member of the whole family of defense logic. This replaces Godel's view that F is interpreted as Provable / F and is equated with x Proofx, F. He believes that this method of converting implicit proof terms into explicit proof terms not only realizes the proper embedding of LP by S4 system. The problem of violation of the second incompleteness theorem by S4 is reasonably solved, and the long expected provable semantics is also provided for S4. After that, Altemov applies the proof logic to cognitive theory. On this basis, other defense logic systems were established and developed, but Altemov did not regard the proof logic as the basic defense logic system. In J, t: F is no longer interpreted as proof that t is a proof of F, but as a defence of F. and t is a proof polynomial of F. It is proved by the argument constant and the defense variable through the monadic operator proof "! When t is only a logical axiom in J, the set of formulas containing all t: F forms is called the constant parameter of J system. All deductions are derived under given constant parameters, Because it specifies the defense term of the axiom. J system semantic model is the Kripke model plus the acceptable evidence function 蔚 n t FG, which is the mapping of the set of defense polynomials and formulas to the possible world, as opposed to such a semantic model. J is reliable and complete. And, By adding the cognitive axioms corresponding to logical consciousness, sufficient rule, positive introspection rule and negative introspection rule to J system, The other defense logic systems J4N J45 JT4 JT4 JT45 and JD45 are also reliable and complete. By converting the mouth F to a special structure such as t: F, the defense logic system avoids the logic omnipotent problem of traditional modal knowledge logic. This allows us to expand our knowledge more safely through defense logic. Based on the proof logic LP and the common multi-agent knowledge logic system TnN S4n and S5n, the defensible knowledge systems TnJN S4Jn and S5nJ can not only let us know the reasons behind the knowledge. The conventional reduction method in its own system also makes the depiction of the acquisition process of public knowledge reasonable and feasible, and makes up for the defects of traditional knowledge logic in theory and practice. It not only reveals the nature of the problem, but also shows its own strong expressive and descriptive ability. Defense logic is a new topic in cognitive logic, and it has great room for development. For example, the development of quantitative defense logic and the establishment and perfection of defence logic system such as S4LPU LPP, etc. Therefore, the research on defense logic has important disciplinary and contemporary significance. This paper systematically combs the development process of defense logic, explains the main contents of defence logic in detail, and evaluates the value of defense logic in the application of philosophy.
【学位授予单位】：南京大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：B81-0

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