本文關(guān)鍵詞： 辯護(hù)邏輯 證明邏輯 邏輯全能 公共知識(shí) 格蒂爾問(wèn)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(hù)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(jìn)程中缺失的辯護(hù)算子作為研究對(duì)象,辯護(hù)邏輯吸收了數(shù)學(xué)證明論和主流的認(rèn)識(shí)論觀點(diǎn),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(gè)辯護(hù)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(gè)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(diǎn)。他認(rèn)為這種把隱式證明項(xiàng)轉(zhuǎn)換成顯式證明項(xiàng)的做法不僅實(shí)現(xiàn)了S4系統(tǒng)對(duì)LP的適當(dāng)嵌入,合理地解決了S4對(duì)第二不完全性定理的違反問(wèn)題,而且也為S4提供了期望已久的可證性語(yǔ)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(hù)邏輯系統(tǒng)。但阿爾捷莫夫并沒(méi)有把證明邏輯作為基本辯護(hù)邏輯系統(tǒng),而是把只包含LP中應(yīng)用和總計(jì)公理的系統(tǒng)J作為標(biāo)準(zhǔn)辯護(hù)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(gè)辯護(hù)。而t是證明多項(xiàng)式,它由辯護(hù)常量和辯護(hù)變量通過(guò)一元算子證明檢驗(yàn)“!”以及二元算子應(yīng)用“·”和結(jié)合“+”組成。當(dāng)t僅是辯護(hù)常量,F是J中的邏輯公理時(shí),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(jìn)行的推導(dǎo),因?yàn)樗付宿q護(hù)公理的辯護(hù)項(xiàng)。J系統(tǒng)的語(yǔ)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(hù)多項(xiàng)式和公式集到可能世界的映射。相對(duì)于這樣的語(yǔ)義模型,J是可靠的和完全的。并且,通過(guò)將邏輯意識(shí)、充分規(guī)則、正自省規(guī)則和負(fù)自省規(guī)則對(duì)應(yīng)的認(rèn)知公理添加于J系統(tǒng)中,得到的其他的辯護(hù)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(hù)邏輯系統(tǒng)避免了傳統(tǒng)模態(tài)知識(shí)邏輯所具有的邏輯全能問(wèn)題,這讓我們可以更安全地通過(guò)辯護(hù)邏輯來(lái)擴(kuò)充自身的知識(shí)。在刻畫公共知識(shí)方面,基于證明邏輯LP與常見的多主體知識(shí)邏輯系統(tǒng)Tn、S4n和S5n之上建立的得到辯護(hù)的知識(shí)系統(tǒng)TnJ、S4Jn和S5nJ,不僅能夠讓我們清楚得到知識(shí)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(shí)的獲得過(guò)程之刻畫變得合理可行,彌補(bǔ)了傳統(tǒng)知識(shí)邏輯在理論和實(shí)踐方面的缺陷。而一階辯護(hù)邏輯對(duì)格蒂爾問(wèn)題的分析,不但揭示了該問(wèn)題的本質(zhì),更展現(xiàn)了它自身強(qiáng)大的表達(dá)刻畫能力。辯護(hù)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(hù)邏輯的發(fā)展,S4LP、LPP等辯護(hù)邏輯系統(tǒng)的建立完善等。因而對(duì)辯護(hù)邏輯的研究具有重要的學(xué)科意義和時(shí)代意義。本文在對(duì)相關(guān)經(jīng)典文獻(xiàn)解讀的基礎(chǔ)上,系統(tǒng)梳理了辯護(hù)邏輯的發(fā)展過(guò)程,詳細(xì)說(shuō)明了辯護(hù)邏輯的主要內(nèi)容,適當(dāng)評(píng)價(jià)了辯護(hù)邏輯在哲學(xué)應(yīng)用方面的價(jià)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(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：B81-0

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相關(guān)期刊論文 前1條

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本文編號(hào)：1544722