The Development of Logic as Reflected in the Fate of the Syllogism 1600–1900

One way to determine the quality and pace of change in a science as it undergoes a major transition is to follow some feature of it which remains relatively stable throughout the process. Following the chosen item as it goes through reinterpretation permits conclusions to be drawn about the nature and scope of the broader change in question. In what follows, this device is applied to the change which took place in logic in the mid-nineteenth century. The feature chosen as the focal point is the categorical syllogism.     

可拓逻辑研究展望

可拓学是由我国学者自主创立的一门新学科,它研究以形式化的模型分析事物拓展的可能性和开拓创新的规律,形成解决矛盾问题的方法。中国科学院权威杂志《科学通报》在评论文章中指出:“可拓学是一门充满生命力的新学科,它的创立是中国人的骄傲,它不仅属于中国,更属于世界。”[1]经过30年的不断开拓,可拓学已经发展成为一门横跨哲学、数学与工程学的交叉学科,我们哲学界也可以积极对相关问题进行科学的研究和探索。本文拟从逻辑的角度谈谈可拓逻辑的研究设想,以期能够引起哲学界、逻辑学界对可拓学研究的关注。一可拓逻辑的研究价值人类的历史…     

A First Order Nonmonotonic Extension of Constructive Logic

Certain extensions of Nelson's constructive logic N with strong negation have recently become important in arti.cial intelligence and nonmonotonic reasoning, since they yield a logical foundation for answer set programming (ASP). In this paper we look at some extensions of Nelson's .rst-order logic as a basis for de.ning nonmonotonic inference relations that underlie the answer set programming semantics. The extensions we consider are those based on 2-element, here-and-there Kripke frames. In particular, we prove completeness for .rst-order here-and-there logics, and their minimal strong negation extensions, for both constant and varying domains. We choose the constant domain version, which we denote by QN^c₅, as a basis for de.ning a .rst-order nonmonotonic extension called equilibrium logic. We establish several metatheoretic properties of QN^c₅, including Skolem forms and Herbrand theorems and Interpolation, and show that the .rst-oder version of equilibrium logic can be used as a foundation for answer set inference.     

逻辑训练对不同理性思维方式大学生三段论推理的影响

采用理性—经验思维方式量表对105名大学生进行测量,选出高、低理性思维方式各35名大学生进行实验,探讨了逻辑训练对不同理性思维方式大学生三段论推理的影响。结果表明：(1)高理性思维方式个体三段论推理的平均反应时快于低理性思维方式个体;非冲突类型题目推理的平均正确率高于冲突类型题目;逻辑训练可以提高个体三段论推理的平均反应时和正确率;(2)逻辑训练后非冲突任务类型题目的平均正确率高于冲突任务类型题目;(3)逻辑训练对低理性思维方式个体冲突任务类型题目平均正确率的提高效果更明显。这意味着逻辑训练可以显著提升个体的推理成绩,但不能完全消除信念偏差对推理的影响,而且逻辑训练对低理性思维方式个体推理成绩的提升效果更加明显。     

A Predicate Logical Extension of a Subintuitionistic Propositional Logic

We develop a predicate logical extension of a subintuitionistic propositional logic. Therefore a Hilbert type calculus and a Kripke type model are given. The propositional logic is formulated to axiomatize the idea of strategic weakening of Kripke's semantic for intuitionistic logic: dropping the semantical condition of heredity or persistence leads to a nonmonotonic model. On the syntactic side this leads to a certain restriction imposed on the deduction theorem. By means of a Henkin argument strong completeness is proved making use of predicate logical principles, which are only classically acceptable.     

Extension Properties and Subdirect Representation in Abstract Algebraic Logic

This paper continues the investigation, started in Lávi?ka and Noguera (Stud Log 105(3): 521–551, 2017), of infinitary propositional logics from the perspective of their algebraic completeness and filter extension properties in abstract algebraic logic. If follows from the Lindenbaum Lemma used in standard proofs of algebraic completeness that, in every finitary logic, (completely) intersection-prime theories form a basis of the closure system of all theories. In this article we consider the open problem of whether these properties can be transferred to lattices of filters over arbitrary algebras of the logic. We show that in general the answer is negative, obtaining a richer hierarchy of pairwise different classes of infinitary logics that we separate with natural examples. As by-products we obtain a characterization of subdirect representation for arbitrary logics, develop a fruitful new notion of natural expansion, and contribute to the understanding of semilinear logics.     

The Refined Extension Principle for Semantics of Dynamic Logic Programming

Over recent years, various semantics have been proposed for dealing with updates in the setting of logic programs. The availability of different semantics naturally raises the question of which are most adequate to model updates. A systematic approach to face this question is to identify general principles against which such semantics could be evaluated. In this paper we motivate and introduce a new such principle the refined extension principle. Such principle is complied with by the stable model semantics for (single) logic programs. It turns out that none of the existing semantics for logic program updates, even though generalisations of the stable model semantics, comply with this principle. For this reason, we define a refinement of the dynamic stable model semantics for Dynamic Logic Programs that complies with the principle.     

范畴三段论推理的表征与影响因素研究

采用纸笔测验法对大学生如何进行范畴三段论推理进行了初步探讨.被试为123名大学生.研究发现:(1)人们在范畴三段论推理中一般有图形(像)的参与,且明晰的图形提示有助于推理成绩的提高;(2)影响范畴三段论推理的因素主要有前提能够建构的模型的数目、前提的内容、前提的格(格效应)和推理者自身(文理科、知识背景等)因素.具体而言,图示只对纯符号推理题有提高作用,理科学生只在文字内容推理题上显著高于文科学生;(3)对前提的不完全解释是产生推理错误的重要原因之一.     

A Formal Reconstruction of Buridan's Modal Syllogism

In this paper, we provide a historical exposition of John Buridan's theory of divided modal propositions. We then develop a semantic interpretation of Buridan's theory which pays particular attention to Buridan's ampliation of modal terms. We show that these semantics correctly capture his syllogistic reasoning.     

编者导言(英文)

This special issue of the journal‘Studies in Logic’ results from an international workshopon‘TheHistory of Logic in China’held in Amsterdam,The Netherlands,on November 24-26, 2010 (http://www.sciencehistory.asia/history-logic-china).This event brought together,     

The Use of Syllogism in Rational-Emotive Therapy

The author indicates how the use of syllogistic logic in rational-emotive therapy can help therapists expose clients' irrational beliefs.     

The Greatest Extension of S4 into which Intuitionistic Logic is Embeddable

This paper gives a characterization of those quasi-normal extensions of the modal system S4 into which intuitionistic propositional logic Int is embeddable by the Gödel translation. It is shown that, as in the normal case, the set of quasi-normal modal companions of Int contains the greatest logic, M*, for which, however, the analog of the Blok-Esakia theorem does not hold. M* is proved to be decidable and Halldén-complete; it has the disjunction property but does not have the finite model property.     

The Is-Ought Problem: An Investigation in Philosophical Logic

Book Information The Is-Ought Problem: An Investigation in Philosophical Logic. By Gerhard Schurz. Kluwer. Dordrecht. 1997. Pp. x + 332. £92.25.     

Game Logic - An Overview

Game Logic is a modal logic which extends Propositional Dynamic Logic by generalising its semantics and adding a new operator to the language. The logic can be used to reason about determined 2-player games. We present an overview of meta-theoretic results regarding this logic, also covering the algebraic version of the logic known as Game Algebra.     

An Incomplete Relevant Modal Logic

The relevant modal logic G is a simple extension of the logic RT, the relevant counterpart of the familiar classically based system T. Using the Routley–Meyer semantics for relevant modal logics, this paper proves three main results regarding G: (i) G is semantically complete, but only with a non-standard interpretation of necessity. From this, however, other nice properties follow. (ii) With a standard interpretation of necessity, G is semantically incomplete; there is no class of frames that characterizes G. (iii) The class of frames for G characterizes the classically based logic T.