Proof Theory of Paraconsistent Quantum Logic

Paraconsistent quantum logic, a hybrid of minimal quantum logic and paraconsistent four-valued logic, is introduced as Gentzen-type sequent calculi, and the cut-elimination theorems for these calculi are proved. This logic is shown to be decidable through the use of these calculi. A first-order extension of this logic is also shown to be decidable. The relationship between minimal quantum logic and paraconsistent four-valued logic is clarified, and a survey of existing Gentzen-type sequent calculi for these logics and their close relatives is addressed.     

The natural history of the understanding: locke and the rise of facultative logic in the eighteenth century

Whatever its merits and difficulties, the concept of logic embedded in much of the ‘new philosophy’ of the early modern period was then understood to supplant contemporary views of formal logic. The notion of compiling a natural history of the understanding constituted the basis of this new concept of logic. The following paper attempts to trace this view of logic through some of the major and numerous minor texts of the period, centering on the development and influence of John Locke's understanding of the analysis of the cognitive faculties as the discipline of logic.     

中国当代归纳逻辑研究概况

我国归纳逻辑的研究始于20世纪初,但直到20世纪80年代初西方现代归纳逻辑传入国内之后,才开启了我国当代归纳逻辑研究的新时代。在这近三十年的研究中,广大归纳逻辑学者围绕着形式与非形式、概率与因果、巴斯卡概率与非巴斯卡概率这些核心问题进行了广泛而深入的探讨,取得了丰硕的成果;此外,在应用研究和逻辑哲学问题研究方面也取得了重要的进展;与此同时,我国学者还积极开展了国际交流与合作,并取得了一定的成绩。     

A cirquent calculus system with clustering and ranking

Cirquent calculus is a new proof-theoretic and semantic approach introduced by G. Japaridze for the needs of his theory of computability logic (CoL). The earlier article “From formulas to cirquents in computability logic” by Japaridze generalized formulas in CoL to circuit-style structures termed cirquents. It showed that, through cirquents with what are termed clustering and ranking, one can capture, refine and generalize independence-friendly (IF) logic. Specifically, the approach allows us to account for independence from propositional connectives in the same spirit as IF logic accounts for independence from quantifiers. Japaridze's treatment of IF logic, however, was purely semantical, and no deductive system was proposed. The present paper syntactically constructs a cirquent calculus system with clustering and ranking, sound and complete w.r.t. the propositional fragment of cirquent-based semantics. Such a system captures the propositional version of what is called extended IF logic, thus being an axiomatization of a nontrivial fragment of that logic.     

台湾六十年(1949-2009)逻辑学研究

本研究汇整近60年(1949-2009)来台湾学者在台湾及大陆地区出版或发表的、与逻辑学有关的书籍、期刊论文、博硕士论文、及翻译作品,并作一综合性的叙述与评论。为撰写本研究报告,作者一共收集了179笔相关的资料;其中专书计有61本,期刊论文计有62篇,博硕士论文计有21篇,翻译作品则有35篇。本研究的内容一共分为6节:第1节说明近60年来由台湾学者所发行与逻辑学相关的专书,时间上横跨1953年至2009年这57年;第2节说明近60年来由台湾学者所发行与逻辑学相关的期刊论文,时间上横跨1964年至2009年这46年;第3节说明近60年来由台湾学者所发行与逻辑学相关的博硕士论文,时间上横跨1986年至2008年这23年;第4节说明近60年来由台湾学者所发行与逻辑学相关的翻译作品,时间上横跨1957年至2008年这52年;第5节则说明在台湾与逻辑学有关的学术组织、以及近几年来开始出现的逻辑学专业会议;第6节为笔者的结论与建议。     

人类非逻辑思维辨析

按照皮亚杰的观点,成人的思维发展已达到“形式运算”的阶段,能够依据形式逻辑规则进行抽象的合乎逻辑的判断和推理。从此以后,根据逻辑的标准判断人类的推理是否是理性的就自然而然被接受了。然而最近的一些研究发现,人类在现实生活中并不完全遵照形式逻辑的规则来思维,在许多时候都表现出非逻辑的一面,似乎有另一种大家公认的“心理逻辑”。但是,非逻辑并不意味着非理性,从生态学的角度说,很多时候心理逻辑具有理性的一面。     

古典自由主义经济的伦理反思

古典自由主义经济理论所建构的经济模式 ,实质上是一种“逻辑一致的理想的客观经济模型”。这一模型通过排除经济行为主体的伦理动机和市场经济运行中的非本质因素 ,同时促进了经济的增长和道德贫困 ,导致了两难选择的伦理困境。因此 ,必须变革古典自由主义经济的基础 ,用“生活的逻辑”置换“资本的逻辑” ,依据“生活的逻辑”保持经济增长与人类美好生活之间合理的伦理张力 ,从而走出古典自由主义经济的伦理困境。     

三值量子逻辑进路探析

量子测量实验显示部分经典逻辑规则在量子世界中失效。标准量子逻辑进路通过特有的希尔伯特空间的格运算揭示出一种内在于微观物理学理论的概念框架结构,也即量子力学测量命题的正交补模或弱模格,解释了经典分配律的失效,它在形式化方面十分完美,但在解释方面产生了一些概念混乱。在标准量子逻辑进路之外,赖欣巴赫通过引入"不确定"的第三真值独立地提出一种不同的量子逻辑模型来解释量子实在的特征,不是分配律而是排中律失效,但是他的三值量子逻辑由于缺乏标准量子逻辑的上述优点而被认为与量子力学的概率空间所要求的潜在逻辑有很少联系。本文尝试引入一种新的三值逻辑模型来说明量子实在,它有以下优点:(1)满足卢卡西维茨创立三值逻辑的最初语义学假定;(2)克服赖欣巴赫三值量子逻辑的缺陷;(3)澄清标准量子逻辑遭遇的概念混乱;(4)充分地保留经典逻辑规则,特别是标准量子逻辑主张放弃的分配律。     

Trance logic in hypnosis and imagination.

In 2 experiments we investigated trance logic, or the tolerance of logical incongruity, in age regression and hallucination. Experiment 1 tested 21 hypnotizable and 19 unhypnotizable subjects in an application of the real-simulating model of hypnosis. Experiment 2 tested 26 high and 19 low imagery ability subjects in an adaptation of the model to the imagination context. Subjects' experiences were investigated through the experiential analysis technique. More real than simulating subjects displayed trance logic during age regression, but they did not differ on the major measures of trance logic during hallucination. This pattern of responding occurred in both the hypnosis and the imagination contexts. Subjects' comments suggested that completeness of and belief in age regression or hallucination may play some role in trance logic. The importance of understanding trance logic from the subject's point of view is discussed.     

马克思劳动人本思想对资本逻辑的批判与超越

不断占有剩余价值以自我增殖,进而无度扩张,这构成资本的内在逻辑。资本提升了劳动能力,改进了劳动方式,变革了全部社会关系,瓦解了封建体系,为人的解放创造了前提。但在资本逻辑支配下,劳动采取异化形式沦为资本增殖的元素,引发资本统治劳动、人为物驭的发展悖论,此一洞见构成马克思劳动人本思想对资本逻辑的批判向度。透过劳动从属资本的迷雾,马克思深度揭示了劳动发展与社会演进和人的本质的内在同一性,确认了劳动者的历史主体地位,指明了经由劳动和劳动者解放实现人的解放以及资本逻辑消亡的必然性,彰显了劳动人本思想以劳动和劳动者为本的价值诉求及对资本逻辑的超越之维。     

Varieties of Linear Calculi

A uniform calculus for linear logic is presented. The calculus has the form of a natural deduction system in sequent calculus style with general introduction and elimination rules. General elimination rules are motivated through an inversion principle, the dual form of which gives the general introduction rules. By restricting all the rules to their single-succedent versions, a uniform calculus for intuitionistic linear logic is obtained. The calculus encompasses both natural deduction and sequent calculus that are obtained as special instances from the uniform calculus. Other instances give all the invertibilities and partial invertibilities for the sequent calculus rules of linear logic. The calculus is normalizing and satisfies the subformula property for normal derivations.     

作为一种分析哲学的数理逻辑——以相对可计算性与随机性概念研究为例

对于现代逻辑的运用是分析哲学的一大特征。分析哲学与现代逻辑甚至具有共同的起源:不仅分析哲学与现代逻辑的奠基者是同一批人,他们曾面对的还是同样的问题,并为此开发出我们所熟知的研究形态。然而,分析哲学和现代逻辑(尤其是数理逻辑)后来的发展似乎走上了不同的道路。笔者则希望论证当代数理逻辑研究仍然保留了分析哲学解决问题的形态——语言分析——的主要特征。论证主要基于两则案例分析,一个是对埃米尔·波斯特(Emil Post)关于可计算性理论的开创性工作,另一个是佩尔·马丁–洛夫(Per Martin-L?f)等人在随机性概念方面的工作。笔者还将进一步提议,仍然存在着一些值得当代分析哲学家和数理逻辑共同关心的问题。     

Mathematical logic in the soviet union, 1917–1980

This essay describes a variety of contributions which relate to the connection of probability with logic. Some are grand attempts at providing a logical foundation for probability and inductive inference. Others are concerned with probabilistic inference or, more generally, with the transmittance of probability through the structure (logical syntax) of language. In this latter context probability is considered as a semantic notion playing the same role as does truth value in conventional logic. At the conclusion of the essay two fully elaborated semantically based constructions of probability logic are presented.     

Does Science Influence the Logic we Ought to Use: A Reflection on the Quantum Logic Controversy

In this article I argue that there is a sense in which logic is empirical, and hence open to influence from science. One of the roles of logic is the modelling and extending of natural language reasoning. It does so by providing a formal system which succeeds in modelling the structure of a paradigmatic set of our natural language inferences and which then permits us to extend this structure to novel cases with relative ease. In choosing the best system of those that succeed in this, we seek certain virtues of such structures such as simplicity and naturalness (which will be explained). Science can influence logic by bringing us, as in the case of quantum mechanics, to make natural language inferences about new kinds of systems and thereby extend the set of paradigmatic cases that our formal logic ought to model as simply and naturally as possible. This can alter which structures ought to be used to provide semantics for such models. I show why such a revolution could have led us to reject one logic for another through explaining why complex claims about quantum mechanical systems failed to lead us to reject classical logic for quantum logic.     

PHILOSOPHIC WARRANTS FOR SCRIPTURAL REASONING

Addressing readers who are already acquainted with the practices of Scriptural Reasoning (SR), this essay offers a logical strategy for warranting and testing such practices as well as all postmodern criticisms of modern inquiry. The strategy is to distinguish the logic of suffering, which is reducible to the binary terms of propositional logic, from the logic of repair, which is not. The essay argues that, if reduced to such binary terms, efforts at repair become inadvertent acts of oppression, or acts that produce suffering. The essay concludes that postmodern and postliberal theorists become inadvertent oppressors when their attempts to repair modern inquiry are presented through propositional logics. The practice of SR should be irreducible to such logics.     

Modal Deduction in Second-Order Logic and Set Theory - II

In this paper, we generalize the set-theoretic translation method for poly-modal logic introduced in [11] to extended modal logics. Instead of devising an ad-hoc translation for each logic, we develop a general framework within which a number of extended modal logics can be dealt with. We first extend the basic set-theoretic translation method to weak monadic second-order logic through a suitable change in the underlying set theory that connects up in interesting ways with constructibility; then, we show how to tailor such a translation to work with specific cases of extended modal logics.     

基于论证型式应用的论证挖掘

本文旨在为构建一种以论证型式为基础的方法,用以帮助非形式逻辑的学生分析自然语言对话的文本,并识别出其中所出现的常见论证类型。他们在这一过程中时常会错误地辨识论证类型,而本文将表明所发展的这种方法对于学习非形式逻辑的学生们是非常有帮助的。另外,对于那些可用于构建一种有用的论证识别方法的理论资源,本文对其最新发展动态进行了考察,并且也概览了当前人工智能领域中所发展的自动论证挖掘工具。     

Husserl’s Foundation of the Formal Sciences in his “Logical Investigations”

This article is composed of three sections that investigate the epistemological foundations of Husserl’s idea of logic from the Logical Investigations. First, it shows the general structure of this logic. Husserl conceives of logic as a comprehensive, multi-layered theory of possible theories that has its most fundamental level in a doctrine of meaning. This doctrine aims to determine the elementary categories that constitute every possible meaning (meaning-categories). The second section presents the main idea of Husserl’s search for an epistemological foundation for knowledge, science and logic. Their epistemological clarification can only be reached through a detailed analysis of the structure of those intentions that give us what is meant in our intentions. To reveal the intuitive giveness of logical forms is the ultimate aim of Husserl’s epistemology of logic. Logical forms and meaning-categories can only be given in a certain higher-order intuition that Husserl calls categorical intuition. The third section of this article distinguishes different kinds of categorical intuition and shows how the most basic logical categories and concepts are given to us in a categorical abstraction.     

Skepticism and Epistemic Logic

This essay attempts to implement epistemic logic through a non-classical inference relation. Given that relation, an account of '(the individual) a knows that A' is constructed as an unfamiliar non-normal modal logic. One advantage to this approach is a new analysis of the skeptical argument.