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.     

Irreflexive Modality in the Intuitionistic Propositional Logic and Novikov Completeness

A. Kuznetsov considered a logic which extended intuitionistic propositional logic by adding a notion of 'irreflexive modality'. We describe an extension of Kuznetsov's logic having the following properties: (a) it is the unique maximal conservative (over intuitionistic propositional logic) extension of Kuznetsov's logic; (b) it determines a new unary logical connective w.r.t. Novikov's approach, i.e., there is no explicit expression within the system for the additional connective; (c) it is axiomatizable by means of one simple additional axiom scheme.     

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.     

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.     

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.     

A Theory of Hypermodal Logics: Mode Shifting in Modal Logic

A hypermodality is a connective whose meaning depends on where in the formula it occurs. The paper motivates the notion and shows that hypermodal logics are much more expressive than traditional modal logics. In fact we show that logics with very simple K hypermodalities are not complete for any neighbourhood frames.     

A Note on Priest's Finite Inconsistent Arithmetics

We give a complete characterization of Priest's Finite Inconsistent Arithmetics observing that his original putative characterization included arithmetics which cannot in fact be realized.     

A Note on Negation in Categorial Grammar

A version of strong negation is introduced into Categorial Grammar.The resulting syntactic calculi turn out to be systems of connexivelogic.     

On the Nature of Continuous Physical Quantities in Classical and Quantum Mechanics

Journal of Philosophical Logic - Within the traditional Hilbert space formalism of quantum mechanics, it is not possible to describe a particle as possessing, simultaneously, a sharp position value...     

A Note on Neat Reducts

SC, CA, QA and QEA denote the class of Pinter’s substitution algebras, Tarski’s cylindric algebras, Halmos’ quasi-polyadic and quasi-polyadic equality algebras, respectively. Let . and . We show that the class of n dimensional neat reducts of algebras in K _m is not elementary. This solves a problem in [2]. Also our result generalizes results proved in [1] and [2]. Presented by Robert Goldblatt     

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。     

Note on the rationality of rule-based versus exemplar-based processing in human judgment

This paper reports a study of the relationship between rule- versus exemplar-based processing and criteria for rationality of judgment. Participants made probability judgments in a classification task devised by S. W. Allen and L. R. Brooks (1991). In the exemplar condition, the miscalibration was accounted for by stochastic components of the judgment with a format-dependence effect, implying simultaneous over- and underconfidence depending on the response scale. In the rule condition, there was an overconfidence bias not accounted for by the stochastic components of judgment. In both conditions the participants were additive on average and reasonably transitive, but the larger stochastic component in the exemplar condition produced somewhat larger absolute deviations. The results suggest that exemplar processes are unbiased but more perturbed by stochastic components, while rule-based processes may be more prone to bias.     

A foundation for support theory based on a non-Boolean event space

A new foundation is presented for the theory of subjective judgments of probability known in the psychological literature as “Support Theory”. It is based on new complementation operations that, unlike those of classical probability theory (set-theoretic complementation) and classical logic (negation), need not satisfy the principles of the Law of The Excluded Middle and the Law of Double Complementation. Interrelationships between the new complementation operations and the Kahneman and Tversky judgmental heuristic of availability are described.     

An Impossibility Theorem on Beliefs in Games

A paradox of self-reference in beliefs in games is identified, which yields a game-theoretic impossibility theorem akin to Russell’s Paradox. An informal version of the paradox is that the following configuration of beliefs is impossible:Ann believes that Bob assumes thatAnn believes that Bob’s assumption is wrongThis is formalized to show that any belief model of a certain kind must have a ‘hole.’ An interpretation of the result is that if the analyst’s tools are available to the players in a game, then there are statements that the players can think about but cannot assume. Connections are made to some questions in the foundations of game theory.Special Issue Ways of Worlds II. On Possible Worlds and Related Notions Edited by Vincent F. Hendricks and Stig Andur Pedersen     

效度概化：预测效度元分析的30年成果述评

效度概化是通过元分析技术对普遍化的预测效度的估计。元分析是研究效度概化问题的技术,是对具有“预测因子-效标”特征的相关数据进行定量综合的方法。效度概化促进了预测因子与效标之间关系的理论研究和应用研究,是应用心理学领域近30年（1977~2007）来最重要的进展之一。30年来的效度概化研究表明,认知能力测验、知识和技能测验、人格测验、结构化面试和评价中心技术等的预测效度具有鲁棒性、对应性和联合增值性     

A Note on Scripture in the Summa theologiae

Beginning with the question of whether Aquinas's  Summa theologiae  inevitably distorts the meaning of biblical texts by removing them from their narrative context, this essay suggests that one way to think about Aquinas's use of Scripture in the  Summa theologiae  is to read together, as an ensemble, the biblical texts that he cites when treating a particular theme. Focusing on his first four questions on the virtue of faith ( ST  II-II, qq. 1–4), I argue that Aquinas's selection of biblical texts from across the canonical Scriptures enables him to provide a nuanced biblical perspective on a particular theme even without finding it necessary to quote Scripture in every article. I seek to bring to light the way that the various biblical texts in the question—whose functions within the articles are widely diverse, from providing the hinge for a  responsio  to framing a minor objection–complement and echo one another.     

A Measure for the Reliability of a Rating Scale Based on Longitudinal Clinical Trial Data

A new measure for reliability of a rating scale is introduced, based on the classical definition of reliability, as the ratio of the true score variance and the total variance. Clinical trial data can be employed to estimate the reliability of the scale in use, whenever repeated measurements are taken. The reliability is estimated from the covariance parameters obtained from a linear mixed model. The method provides a single number to express the reliability of the scale, but allows for the study of the reliability’s time evolution. The method is illustrated using a case study in schizophrenia. The authors are grateful to J&J PRD for kind permission to use their data. We gratefully acknowledge support from the Belgian IUAP/PAI network “Statistical Techniques and Modeling for Complex Substantive Questions with Complex Data.”     

A Note on Finiteness in the Predicative Foundations of Arithmetic

Recently, Feferman and Hellman (and Aczel) showed how to establish the existence and categoricity of a natural number system by predicative means given the primitive notion of a finite set of individuals and given also a suitable pairing function operating on individuals. This short paper shows that this existence and categoricity result does not rely (even indirectly) on finite-set induction, thereby sustaining Feferman and Hellman's point in favor of the view that natural number induction can be derived from a very weak fragment of finite-set theory, so weak that finite-set induction is not assumed. Many basic features of finiteness fail to hold in these weak fragments, conspicuously the principle that finite sets are in one-one correspondence with a proper initial segments of a (any) natural number structure. In the last part of the paper, we propose two prima facie evident principles for finite sets that, when added to these fragments, entail this principle.     

基础概率在贝叶斯推理中的作用

针对贝叶斯推理研究中基础概率忽略现象的争论,直接操纵基础概率水平,考察被试在贝叶斯推理时是否加工了基础概率信息。结果表明,低基础概率组后验概率估计显著低,无基础概率组后验概率估计反应时显著短于有基础概率组。被试在各种条件下估计的正确率都较低,说明对基础概率在贝叶斯推理中的作用考虑不充分。