本文關(guān)鍵詞： 辯護邏輯 證明邏輯 邏輯全能 公共知識 格蒂爾問題　出處：《南京大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

【摘要】：辯護邏輯是用于認(rèn)知推理的邏輯系統(tǒng)群。以在傳統(tǒng)邏輯形式化進程中缺失的辯護算子作為研究對象,辯護邏輯吸收了數(shù)學(xué)證明論和主流的認(rèn)識論觀點,在古典命題邏輯的基礎(chǔ)上建立發(fā)展。證明邏輯LP是整個辯護邏輯家族譜系中最早的成員。它的建立源于阿爾捷莫夫把口F解釋成Proof(t,F)這樣一個關(guān)系函數(shù)的想法,這替換了哥德爾將口F解釋成Provable (F),并將其等同于xProof(x, F)的觀點。他認(rèn)為這種把隱式證明項轉(zhuǎn)換成顯式證明項的做法不僅實現(xiàn)了S4系統(tǒng)對LP的適當(dāng)嵌入,合理地解決了S4對第二不完全性定理的違反問題,而且也為S4提供了期望已久的可證性語義學(xué)。之后,阿爾捷莫夫?qū)⒆C明邏輯應(yīng)用于認(rèn)知論中,并在此基礎(chǔ)上建立發(fā)展了其他的辯護邏輯系統(tǒng)。但阿爾捷莫夫并沒有把證明邏輯作為基本辯護邏輯系統(tǒng),而是把只包含LP中應(yīng)用和總計公理的系統(tǒng)J作為標(biāo)準(zhǔn)辯護邏輯系統(tǒng)。在J中,t：F不再解釋成t是F的證明,而是解釋成t是F的一個辯護。而t是證明多項式,它由辯護常量和辯護變量通過一元算子證明檢驗“!”以及二元算子應(yīng)用“·”和結(jié)合“+”組成。當(dāng)t僅是辯護常量,F是J中的邏輯公理時,包含所有t：F形式的公式集合稱為J系統(tǒng)的常量參數(shù)。在該系統(tǒng)中,所有的推導(dǎo)都是在給定常量參數(shù)下進行的推導(dǎo),因為它指定了辯護公理的辯護項。J系統(tǒng)的語義模型是克里普克模型加上可接受證據(jù)函數(shù)ε(t,F),后者是辯護多項式和公式集到可能世界的映射。相對于這樣的語義模型,J是可靠的和完全的。并且,通過將邏輯意識、充分規(guī)則、正自省規(guī)則和負(fù)自省規(guī)則對應(yīng)的認(rèn)知公理添加于J系統(tǒng)中,得到的其他的辯護邏輯系統(tǒng)J4、J45、JT、JT4、JT45和JD45也是可靠的和完全的。由于把口F轉(zhuǎn)換成t：F這樣的特殊結(jié)構(gòu),辯護邏輯系統(tǒng)避免了傳統(tǒng)模態(tài)知識邏輯所具有的邏輯全能問題,這讓我們可以更安全地通過辯護邏輯來擴充自身的知識。在刻畫公共知識方面,基于證明邏輯LP與常見的多主體知識邏輯系統(tǒng)Tn、S4n和S5n之上建立的得到辯護的知識系統(tǒng)TnJ、S4Jn和S5nJ,不僅能夠讓我們清楚得到知識背后的原因,其自身系統(tǒng)中所帶有的常規(guī)削減法也令公共知識的獲得過程之刻畫變得合理可行,彌補了傳統(tǒng)知識邏輯在理論和實踐方面的缺陷。而一階辯護邏輯對格蒂爾問題的分析,不但揭示了該問題的本質(zhì),更展現(xiàn)了它自身強大的表達刻畫能力。辯護邏輯是認(rèn)知邏輯中的新興課題,它還有很大的發(fā)展空間,比如量化辯護邏輯的發(fā)展,S4LP、LPP等辯護邏輯系統(tǒng)的建立完善等。因而對辯護邏輯的研究具有重要的學(xué)科意義和時代意義。本文在對相關(guān)經(jīng)典文獻解讀的基礎(chǔ)上,系統(tǒng)梳理了辯護邏輯的發(fā)展過程,詳細(xì)說明了辯護邏輯的主要內(nèi)容,適當(dāng)評價了辯護邏輯在哲學(xué)應(yīng)用方面的價值。
[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.
【學(xué)位授予單位】：南京大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：B81-0

【參考文獻】

相關(guān)期刊論文 前1條

1 李娜;李巍;;量化核證邏輯QLP概觀[J];重慶理工大學(xué)學(xué)報(社會科學(xué));2014年03期

，

本文編號：1544722