A Note on Binary Inductive Logic

We consider the problem of induction over languages containing binary relations and outline a way of interpreting and constructing a class of probability functions on the sentences of such a language. Some principles of inductive reasoning satisfied by these probability functions are discussed, leading in turn to a representation theorem for a more general class of probability functions satisfying these principles.     

Inductive countersupport

The basic idea by means of which Popper and Miller proved the non-existence of inductive probabilistic support in 1983/1985/1987, is used to prove that inductive probabilistic countersupport does exist. So it seems that after falsification has won over verification on the deductive side of science, countersupport wins over support on the inductive side.     

Algebraic Semantics for Deductive Systems

The notion of an algebraic semantics of a deductive system was proposed in [3], and a preliminary study was begun. The focus of [3] was the definition and investigation of algebraizable deductive systems, i.e., the deductive systems that possess an equivalent algebraic semantics. The present paper explores the more general property of possessing an algebraic semantics. While a deductive system can have at most one equivalent algebraic semantics, it may have numerous different algebraic semantics. All of these give rise to an algebraic completeness theorem for the deductive system, but their algebraic properties, unlike those of equivalent algebraic semantics, need not reflect the metalogical properties of the deductive system. Many deductive systems that don't have an equivalent algebraic semantics do possess an algebraic semantics; examples of these phenomena are provided. It is shown that all extensions of a deductive system that possesses an algebraic semantics themselves possess an algebraic semantics. Necessary conditions for the existence of an algebraic semantics are given, and an example of a protoalgebraic deductive system that does not have an algebraic semantics is provided. The mono-unary deductive systems possessing an algebraic semantics are characterized. Finally, weak conditions on a deductive system are formulated that guarantee the existence of an algebraic semantics. These conditions are used to show that various classes of non-algebraizable deductive systems of modal logic, relevance logic and linear logic do possess an algebraic semantics.     

Emergence of Information Transfer by Inductive Learning

We study a simple game theoretic model of information transfer which we consider to be a baseline model for capturing strategic aspects of epistemological questions. In particular, we focus on the question whether simple learning rules lead to an efficient transfer of information. We find that reinforcement learning, which is based exclusively on payoff experiences, is inadequate to generate efficient networks of information transfer. Fictitious play, the game theoretic counterpart to Carnapian inductive logic and a more sophisticated kind of learning, suffices to produce efficiency in information transfer.     

Categorical Abstract Algebraic Logic: Equivalent Institutions

A category theoretic generalization of the theory of algebraizable deductive systems of Blok and Pigozzi is developed. The theory of institutions of Goguen and Burstall is used to provide the underlying framework which replaces and generalizes the universal algebraic framework based on the notion of a deductive system. The notion of a term -institution is introduced first. Then the notions of quasi-equivalence, strong quasi-equivalence and deductive equivalence are defined for -institutions. Necessary and sufficient conditions are given for the quasi-equivalence and the deductive equivalence of two term -institutions, based on the relationship between their categories of theories. The results carry over without any complications to institutions, via their associated -institutions. The -institution associated with a deductive system and the institution of equational logic are examined in some detail and serve to illustrate the general theory.     

概率逻辑与模糊逻辑在精细化学习诊断中的对比研究

精细化学习诊断有助于客观准确探究学生学习现状,为实施有针对性的补救教学提供理论和数据支持。本文对比研究概率逻辑与模糊逻辑在精细化学习诊断中的表现。首先,从“概念”视角介绍和对比两种逻辑。其次,介绍两个分别基于上述两逻辑的代表性模型：HO-PINC和Fuzzy-DINA。然后,对比两模型在五个实证数据上表现。最后,通过模拟研究进一步对比两模型的心理计量学性能。DIC等模型-数据拟合指标和RMSE等参数返真性指标的结果表明两模型对同一批数据有较一致的分析结果。建议实践者忽略模型选择对数据分析的影响,从概念或思辨视角入手选择使用概率逻辑或模糊逻辑来定义属性。     

归纳推理的抽样理论

作者提出归纳推理的抽样理论,认为归纳推理实质是根据与归纳特征有关的抽样样本情况来推断结论类别具有归纳特征的可能性,其中的抽样可分为类别抽样和特征抽样两种。以大学生为被试的两个实验结果一致支持抽样理论而不是别的归纳推理理论。对于归纳推理的主要现象,抽样理论比其它的相似性解释具有更大的解释范围,特别是能够解释其它理论严格不能解释的归纳推理非对称性现象     

Cultural Difference in Stereotype Perceptions and Performances in Nonverbal Deductive Reasoning and Creativity

A total of 182 undergraduate students from China and the United States participated in a study examining the presence of stereotypical perceptions regarding creativity and deductive reasoning abilities, as well as the influence of stereotype on participants' performance on deductive reasoning and creativity in nonverbal form. The results showed that participants from both China and the United States believed that Americans have better creativity abilities than Chinese and that Chinese have better deductive reasoning skills than Americans. Significant cultural difference in the performances on the measures of creativity was found. The cultural difference in deductive reasoning was found between Chinese participants in China and the Caucasian (not the Asian) participants in the United States, which were somewhat congruent to the stereotypical perceptions. However, the study did not find that stereotypic perceptions directly influenced participants' performance on deductive reasoning and creativity.     

Categorical Abstract Algebraic Logic: Prealgebraicity and Protoalgebraicity

Two classes of π are studied whose properties are similar to those of the protoalgebraic deductive systems of Blok and Pigozzi. The first is the class of N-protoalgebraic π-institutions and the second is the wider class of N-prealgebraic π-institutions. Several characterizations are provided. For instance, N-prealgebraic π-institutions are exactly those π-institutions that satisfy monotonicity of the N-Leibniz operator on theory systems and N-protoalgebraic π-institutions those that satisfy monotonicity of the N-Leibniz operator on theory families. Analogs of the correspondence property of Blok and Pigozzi for π-institutions are also introduced and their connections with preand protoalgebraicity are explored. Finally, relations of these two classes with the (, N)-algebraic systems, introduced previously by the author as an analog of the -algebras of Font and Jansana, and with an analog of the Suszko operator of Czelakowski for π-institutions are also investigated. Presented by Josep Maria Font     

归纳推理多样性效应的发展及其争论

归纳推理多样性效应指的是在归纳论断中,前提项目数量越多、越多样,将能构成归纳力度越强的推理。已有研究表明成人的归纳推理明显受到前提项目多样性的影响,而幼儿的相关研究却存在着两种对立的观点：一是认为幼儿不能基于多样性进行推理,二是认为5岁左右的幼儿就能够基于多样性进行推理。出现此争论的原因可能与研究方法方面的差异有关,如实验范式与前提组间差异、实验材料类别与概念范畴、属性特征及呈现方式、推理形式;此外,儿童的知识经验也是一个影响因素。未来研究可以结合相关领域的研究范式;深入挖掘影响儿童表现出多样性效应的因素;将任务设计多样化;将实验任务的计分方式多样化;开展相关的应用研究。     

A Propositional Dynamic Logic with Qualitative Probabilities

This paper presents an -completeness theorem for a new propositional probabilistic logic, namely, the dynamic propositional logic of qualitative probabilities (D Q P), which has been introduced by the author as a dynamic extension of the logic of qualitative probabilities (Q P) introduced by Segerberg.     

THOG问题的演译结构及其非Wason-Brooks判定方法

本文探讨THOG问题的演绎结构及其非Wason-Brooks判断方法,据于Wason-Brooks判断程序和THOG问题逻辑结构的分析导致如下结论：1．Wason-BrooksTHOG判定方法并非判定THOG的唯一方法;2、被试选择那一种演绎判定模式取决于被试如何对原问题进行等效表征转换;3．判断失败可能意味着被试存在短时记忆容量障碍或者等效表征转换障碍。     

对归纳推理贝叶斯模型的检验

作者用实验比较检验特征归纳的贝叶斯模型、关联相似性模型、基于特征的归纳推理模型和相似性覆盖模型这四种模型。以大学生为被试的实验结果表明：1）在强关联强度一致时,被试的归纳推理基本符合贝叶斯模型和关联相似性模型的预测,在弱关联强度一致时,不符合这四种模型预测;2）在关联强度不一致时,关联强度效应不符合贝叶斯模型的预测;3）在关联强度一致时,贝叶斯模型和关联相似性模型的预测结果是一致的,不能区分两个模型。实验结果较多地支持贝叶斯模型和关联相似性模型。     

A Note on the Interpolation Property in Tense Logic

It is proved that all bimodal tense logics which contain the logic of the weak orderings and have unbounded depth do not have the interpolation property.     

对归纳推理非对称性现象的特征迁移解释

作者创新提出对归纳推理非对称性现象的特征迁移解释,认为根据由前提类别已知的特征集合构成的特征样本中迁移出现在结论类别中的特征的比例,能预测作为新特征的归纳特征由前提类别迁移到结论类别的可能性。以大学生为被试的实验结果支持对非对称性现象的特征迁移解释而不是原来的两种相似性解释。     

A Note on Graded Modal Logic

We introduce a notion of bisimulation for graded modal logic. Using this notion, the model theory of graded modal logic can be developed in a uniform manner. We illustrate this by establishing the finite model property and proving invariance and definability results.