如何利用广义量词的语义性质判断扩展三段论的有效性

在国内外最新研究成果的基础上,笔者通过对文中的定理和推论的证明,主要说明了以下几点：（1）利用广义量词的相关语义性质,比如单调性和对称性,既可以解释亚氏三段论的有效性,又可以解释带有广义量词的扩展三段论的有效性;（2）一些有效的扩展三段论仅仅表征了广义量词的左或右单调性,还有一些有效的扩展三段论同时表征了广义量词的多个语义性质;（3）利用广义量词的东南或西北或西南或东北方向的单调性可以判断一些带有限制条件的扩展三段论的有效性。此研究将有利于广义量词理论的发展,对于计算机科学中的知识表示和知识推理的研究都具有较为重要的理论价值和实践意义。     

广义量词的相关性质研究

本文是笔者对S.Peters与D.Westerst(?)hl([7])的成果的拓展研究。首先介绍相关的概念。其次,笔者详细证明了类型为〈1,1〉的广义量词的对称性与单调性的关系定理。然后,笔者给出了该类量词的余对称性、余相交性和余驻留性定义,接着笔者提出并证明了关于这三个性质的四个定理,而且还详细证明了余对称性与单调性的关系定理。最后,笔者探讨了具有(余)驻留性和(余)对称性的〈1,1〉类型的广义量词的数字三角形的特点。由于〈1,1〉类型的广义量词在自然语言中普遍存在,所以,本文的研究对广义量词理论的发展具有一定的理论价值,对自然语言的计算机信息处理也具有一定的实践指导意义。     

包含广义量词的关系三段论

本文介绍一种推导有效关系三段论格式的方法,这种方法建基于广义量词理论和命题逻辑的一些基本原理,包括代入法、演绎定理、前提代换、引入存在假设、等价变换等。本文显示利用此方法,不仅可推导包含经典量词的关系三段论,还可推导出包含非经典量词(例如数值量词、比例量词、模糊量词)的关系三段论。除了讨论包含一般二元谓词的关系三段论外,本文也讨论了包含比较形容词的关系三段论,同时也证明了上述方法的有效性,并讨论了进一步研究的方向。     

三支论式及因明学说实质之辨析

本文从卢卡西维茨关于亚氏三段论的分析出发,针对学术界中“三支论式”是三段论推理、充分条件假言推理、假言转为三段论推理或外设三段论推理等观点,从工具的使用到工具的锻造这一角度,进行了分析研究。笔者提出了一些与传统看法不同的观点,并在此基础上得出了“三支论式”及因明学说的实质是论证而不是推理的新见解。     

论佛教逻辑中推论前提的真实性问题

本文将陈那、法称因明与西方传统的三段论相比较,指出佛教逻辑从推论前提是否为真的角度来建立推论的基本规则即因三相;西方传统的三段论从形式是否有效的角度来建立推论的一般规则,这反映了佛教逻辑与西方逻辑的根本差异。本文首先指出佛教逻辑中的典型谬误即似因并非形式谬误,其致误之由在于前提为假。佛教逻辑从实质的角度来探讨有效性,不同于西方逻辑形式有效性的概念。佛教逻辑所说的推论其实都是论证。推论前提的真在何种程度上得到因三相的保证,又因陈那、法称因三相的不同而有区别。陈那的因后二相由于除宗有法的限制,只是前提为真的一种例证,其推论并非演绎;法称的因三相则全面保证了前提的真,其推论达到了演绎。法称恰恰是通过剖析推论前提为真的知识论基础从而改造了陈那因明,这体现了佛教逻辑的知识论性格。实际上,佛教逻辑关注前提的真,这已经预示了它在历史的发展中向佛教知识论（量论）的必然转化。     

多级语义量词对心理测量适合度的调查分析

为研究适合心理测量使用的语义量词等级数目而进行了本实验。实验采用自编《词义理解简明量表》,通过180名士兵对多级语义量词的区间赋值和点赋值,对不同等级语义量词模糊度进行了比较性研究。结果发现：(1)区间赋值范围与点赋值95％、99％可信区间无显著差异;(2)语义量词内序列蓑系与自然语言的序列关系基本一致,但词与词赋值区间并不完全等距;(3)三级与六级、七级语义量词的模糊度差异显著,六、七级语义量词模糊度高,在一定程度上不适合用于士兵心理测量。     

工作记忆、表达方式和同质性对线性三段论推理影响的眼动研究

采用眼动记录法,探讨了工作记忆、两个前提间的关系以及表达方式对线性三段论推理的影响。本实验采用2（表达方式：肯定、否定）×2（前提间的关系：同质、不同质）×2（工作记忆容量：高、低）的混合设计。通过分析总注视时间、第一次注视时间、第二次注视时间和回视,发现线性三段论推理过程既有语言加工的参与又有表象加工的参与。推理过程中的语言表征过程和空间关系的建立都受到工作记忆容量的影响,被试的工作记忆容量越高,就越容易建立语言表征和空间的关系。     

条件句的组合性

哲学家认为一种语言必须符合组合原则才能为人所掌握。为了证明这一结论,语言学家希金博瑟姆（J. Higginbotham）仔细检视了自然语言量化条件句是否符合组合性的问题。他通过论证认为,量化条件句要保持组合性必须满足两个假定：前件反事实不相干于后件,条件句排中律。但是他不能为这两个假定提供可靠的基础,因此认为量化条件句是否符合组合性仍是一个问题。然而,希金博瑟姆的论证尽管有其价值却包含了错误。本文将对希金博瑟姆的论证给以纠正,并认为自然语言条件句是充满歧义和模糊的,必须通过释义的方式才可以使它符合组合性。在一定条件下自然语言条件句可以符合组合性,这是由于语义先于语法决定的。     

中学生直言性质三段论推理能力发展的调查研究

一、研究目的、方法和被试用逻辑推理题对中学生进行测试,将测试结果作数理统计处理,可以对各年级学生、男女学生、文理科学生之间的推理水平进行比较研究;并对学生推理能力与不同格的推理形式之间关系,以及与学生的推理能力与学习成绩的关系等问题进行一些探索,从而探求学生思维发展的某些规律.为此,我们设计并进行了这次调查研究.采用问卷法。内容是20道直言性质三段论推理(以下简称三段论推理)题.其中包括:1、四个格的推理题,各四题,每格含推论正确和推论错误的试题各两题.如:“所有的物体都是有重量的,所有的气体都是物体,所以,所有的气体都是有重     

三段论推理中的个体内在影响因素

推理是人们认知的根本。人们在推理过程中,受到许多因素的影响,大致可以分为内在（个体差异）因素和外在（任务）因素。该文主要针对影响三段论推理的内在因素（个体差异）进行评论,并且讨论了将来的研究方向。     

Illusory inferences with quantifiers

The psychological study of reasoning with quantifiers has predominantly focused on inference patterns studied by Aristotle about two millennia ago. Modern logic has shown a wealth of inference patterns involving quantifiers that are far beyond the expressive power of Aristotelian syllogisms, and whose psychology should be explored. We bring to light a novel class of fallacious inference patterns, some of which are so attractive that they are tantamount to cognitive illusions. In tandem with recent insights from linguistics that quantifiers like “some” are treated as wh-questions, these illusory inferences are predicted by the erotetic theory of reasoning, which postulates that a process akin to question asking and answering is behind human inference making.     

Aristotelian diagrams for semantic and syntactic consequence

Several authors have recently studied Aristotelian diagrams for various metatheoretical notions from logic, such as tautology, satisfiability, and the Aristotelian relations themselves. However, all these metalogical Aristotelian diagrams focus on the semantic (model-theoretical) perspective on logical consequence, thus ignoring the complementary, and equally important, syntactic (proof-theoretical) perspective. In this paper, I propose an explanation for this discrepancy, by arguing that the metalogical square of opposition for semantic consequence exhibits a natural analogy to the well-known square of opposition for the categorical statements from syllogistics, but that this analogy breaks down once we move from semantic to syntactic consequence. I then show that despite this difficulty, one can indeed construct metalogical Aristotelian diagrams from a syntactic perspective, which have their own, equally elegant characterization in terms of the categorical statements. Finally, I construct several metalogical Aristotelian diagrams that incorporate both semantic and syntactic consequence (and their interaction), and study how they are influenced by the underlying logical system’s soundness and/or completeness. All of this provides further support for the methodological/heuristic perspective on Aristotelian diagrams, which holds that the main use of these diagrams lies in facilitating analogies and comparisons between prima facie unrelated domains of investigation.

     

Complexly fractionated syllogistic quantifiers

Consider syllogisms in which fraction (percentage) quantifiers are permitted in addition to universal and particular quantifiers, and then include further quantifiers which are modifications of such fractions (such as “almost 1/2 the S are P” and “Much more than 1/2 the S are P”). Could a syllogistic system containing such additional categorical forms be coherent? Thompson's attempt (1986) to give rules for determining validity of such syllogisms has failed; cf. Carnes &; Peterson (forthcoming) for proofs of the unsoundness and incompleteness of Thompson's rules. Building on Peterson (1985), the coherence of such a syllogistic can, however, be demonstrated with an algebra which provides its semantics; e.g., “almost 1/2 the S are P” is represented as “?(3(SP)?SP)”.     

Inhibitory mechanism of the matching heuristic in syllogistic reasoning

A number of heuristic-based hypotheses have been proposed to explain how people solve syllogisms with automatic processes. In particular, the matching heuristic employs the congruency of the quantifiers in a syllogism — by matching the quantifier of the conclusion with those of the two premises. When the heuristic leads to an invalid conclusion, successful solving of these conflict problems requires the inhibition of automatic heuristic processing. Accordingly, if the automatic processing were based on processing the set of quantifiers, no semantic contents would be inhibited. The mental model theory, however, suggests that people reason using mental models, which always involves semantic processing. Therefore, whatever inhibition occurs in the processing implies the inhibition of the semantic contents.     

A Taxonomy of Part-Whole Relations

A taxonomy of part-whole or meronymic relations is developed to explain the ordinary English-speaker's use of the term “part of” and its cognates. The resulting classification yields six types of meronymic relations: 1. component-integral object (pedal-bike), 2. member-collection (ship-fleet), 3. portion-mass (slice-pie), 4. stuff-object (steel-car), 5. feature-activity (paying-shopping), and 6. place-area (Everglades-Florida). Meronymic relations ore further distinguished from other inclusion relations, such as spatial inclusion, and class inclusion, and from several other semantic relations: attribution, attachment, and ownership. This taxonomy is then used to explain cases of apparent intransitivity in merological syllogisms, and standard form syllogisms whose premises express different inclusion relations. The data suggest that intransitivities arise due to equivocations between different types of semantic relations. These results are then explained by means of the relation element theory which accounts for the character and behavior of semantic relations in terms of more primitive relational elements. The inferential phenomena observed are then explained by means of a single principle of element matching.     

古典对当方阵和广义量词

古典对当方阵可同溯到亚里士多德逻辑,并且自此后就一直被广泛地讨论,特别是在中世纪和现代。它刻画了所有、没有、并非所有和某些这四个量词之间的特定逻辑关系,即对当关系。亚里十多德和传统逻辑学家,以及人多数当代语言学家,都把“所有”看作具有存在预设,也即“所有A是B”可以推山“存在A”,而现代逻辑则放弃了这一假定。用现代逻辑对“所有”的解释来代替亚里十多德的解释（对“并非所有”也可以作类似处理）,就产生了现代版本的对当方阵。近年来有许多争论,探讨这两个方阵中哪一个是正确的。本文中我的主要观点是,这个问题不是,或者不应该主要是关于存在预设的,毋宁说它是关于否定的模式的。我认为现代方阵表述了自然语言中否定的一般模式,而传统方阵则没有做到这一点。明乎此,不仅需要把对当方阵应用于四个亚里士多德量词,还需要把它应用到这一类型的广义量词上。现代方阵上的任一量词所展示的否定的模式,常常不是在传统方阵中发现的对当关系。本文提供了一些技术性结果和工具,阐述了解释各种英语限定词的量词方阵的若干例子。本文最后一个例子引入了否定的第二模式。它伴随特定复杂量词出现,也能够在方阵中被表达。     

Theories of categorical reasoning and extended syllogisms

The aim of this study was to examine the predictions of three theories of human logical reasoning, (a) mental model theory, (b) formal rules theory (e.g., PSYCOP), and (c) the probability heuristics model, regarding the inferences people make for extended categorical syllogisms. Most research with extended syllogisms has been restricted to the quantifier “All” and to an asymmetrical presentation. This study used three-premise syllogisms with the additional quantifiers that are used for traditional categorical syllogisms as well as additional syllogistic figures. The predictions of the theories were examined using overall accuracy as well as a multinomial tree modelling technique. The results demonstrated that all three theories were able to predict response selections at high levels. However, the modelling analyses showed that the probability heuristics model did the best in both Experiments 1 and 2.     

Aristotle's Syllogistic and Core Logic

I use the Corcoran–Smiley interpretation of Aristotle's syllogistic as my starting point for an examination of the syllogistic from the vantage point of modern proof theory. I aim to show that fresh logical insights are afforded by a proof-theoretically more systematic account of all four figures. First I regiment the syllogisms in the Gentzen–Prawitz system of natural deduction, using the universal and existential quantifiers of standard first-order logic, and the usual formalizations of Aristotle's sentence-forms. I explain how the syllogistic is a fragment of my (constructive and relevant) system of Core Logic. Then I introduce my main innovation: the use of binary quantifiers, governed by introduction and elimination rules. The syllogisms in all four figures are re-proved in the binary system, and are thereby revealed as all on a par with each other. I conclude with some comments and results about grammatical generativity, ecthesis, perfect validity, skeletal validity and Aristotle's chain principle.     

MOST intelligent people are accurate and SOME fast people are intelligent.: Intelligence,working memory,and semantic processing of quantifiers from a computational perspective

The paper explores the relationship between intelligence and the semantic processing of natural language quantifiers. The first study revealed that intelligence is positively associated with the subjects' performance when solving a picture verification task with one of the four types of sentences: Aristotelian (e.g. ‘All cars are red’), parity (e.g. ‘An even number of cars are red’), numerical (e.g. ‘More than five cars are red’), and proportional (‘More than half of the cars are red’). The strongest relationship was observed between the cognitive ability and the accuracy of proportional sentences, in accordance with the computational theory which predicts the highest engagement of working memory (WM) within the group of proportional quantifiers. Moreover, individuals with higher intelligence reacted faster, but this was observed only in case of quantifiers with low complexity. Exploring further, in the second study we found that WM and intelligence were both significant predictors of subjects' score on proportional sentences. In the third study, we examined the relationships between quantifiers, intelligence, short-term memory (STM), and executive control function. STM was correlated with all types of quantifiers that need counting and keeping track of elements (parity, numerical, and proportional). Only proportional quantifiers were associated with cognitive control. The obtained results are discussed within the computational paradigm of language processing.