Quantifiers and Congruence Closure

We prove some results about the limitations of the expressive power of quantifiers on finite structures. We define the concept of a bounded quantifier and prove that every relativizing quantifier which is bounded is already first-order definable (Theorem 3.8). We weaken the concept of congruence closed (see [6]) to weakly congruence closed by restricting to congruence relations where all classes have the same size. Adapting the concept of a thin quantifier (Caicedo [1]) to the framework of finite structures, we define the concept of a meager quantifier. We show that no proper extension of first-order logic by means of meager quantifiers is weakly congruence closed (Theorem 4.9). We prove the failure of the full congruence closure property for logics which extend first-order logic by means of meager quantifiers, arbitrary monadic quantifiers, and the Härtig quantifier (Theorem 6.1).     

Cognitive, Linguistic, and Social Aspects of Adults' Noun Definitions

Low-income, rural adults and middle-income, urban adults provided oral definitions for eight common nouns. Two general issues were addressed: (1) whether the rural adults' definitions would conform to the well-documented Aristotelian form typically found among middle-class, well-educated adults; and (2) whether different definitional types would emerge for two different noun classes, social vs. object nouns. Participants' definitions were examined for conceptual content and linguistic form. Among rural participants, the mean proportion of definitions conforming to the Aristotelian model was .13, contrasted with .69 for the urban participants. Also, rural adults were significantly less likely to cast definitions in the conventional linguistic form than were urban adults. On other measures of definitional skill as well, rural participants demonstrated less mastery. There were no significant differences in definitional form between social and object nouns. Various explanations for the findings are considered.     

成功老化内涵及影响因素分析

本文在Rowe和Kahn成功老化模型的基础上,结合中国文化背景,提出了生理健康、心理功能、社会参与、生活满意度的四维度成功老化模型。人口学特征、早期经历、社会互动环境、社会历史文化等被动因素,生活方式和习惯、认知活动与训练、老化态度等主动因素,都会影响老年人的成功老化。成功老化是老年人为之奋斗的目标,积极老化是通往该目标的途径。     

Comparing Inductive and Circular Definitions: Parameters,Complexity and Games

Gupta-Belnap-style circular definitions use all real numbers as possible starting points of revision sequences. In that sense they are boldface definitions. We discuss lightface versions of circular definitions and boldface versions of inductive definitions.     

Syntactical Constraints on Definitions

This essay considers arguments for and against syntactical constraints on the proper formalization of definitions, originally owing to Alfred Tarski. It discusses and refutes an application of the constraints generalized to include a prohibition against not only object‐place but also predicate‐place variables in higher‐order logic in a criticism of a recent effort to define the concept of heterologicality in a strengthened derivation of Grelling's paradox within type theory requirements. If the objections were correct, they would offer a more general moral for the proper formal definition of terms in philosophical logic. The criticism nevertheless seems mistaken both in the substance and specific application with respect to legitimate synctactical constraints on definitions of key concepts in the case of Grelling's paradox. As such, the critique provides no justification for overturning previous conclusions concerning the possibility of resurrecting a type‐observant version of Grelling's heterologicality paradox.     

IN PRAISE OF A LOGIC OF DEFINITIONS THAT TOLERATES Ω‐INCONSISTENCY

I argue that a general logic of definitions must tolerate ω‐inconsistency. I present a semantical scheme, , under which some definitions imply ω‐inconsistent sets of sentences. I draw attention to attractive features of this scheme, and I argue that yields the minimal general logic of definitions. I conclude that any acceptable general logic should permit definitions that generate ω‐inconsistency. This conclusion gains support from the application of to the theory of truth.     

Definitions of bullying: Age and sex differences in a Turkish sample

The aim of the present study was to investigate the meaning profile of the Turkish term ‘zorbal?k’, which is considered the most similar to the English word ‘bullying’, and of five other terms in Turkish that describe bullying‐like behaviours. We used the cartoon methodology of a previous study, but with an expanded task of 40 stick‐figure cartoons. These cartoons were shown to 124 students (70 girls and 54 boys), in fourth grade (M = 9.3 years) and eighth grade (M = 13.3 years). Our findings indicated four major clusters: neutral or non‐aggressive, physically aggressive, verbally aggressive, and social exclusion, with the physically‐aggressive cluster splitting into two clusters, physical bullying and other physical aggression, in the older students.     

Amending Frege’s <Emphasis Type="Italic">Grundgesetze der Arithmetik</Emphasis>

Frege’s Grundgesetze der Arithmetik is formally inconsistent. This system is, except for minor differences, second-order logic together with an abstraction operator governed by Frege’s Axiom V. A few years ago, Richard Heck showed that the ramified predicative second-order fragment of the Grundgesetze is consistent. In this paper, we show that the above fragment augmented with the axiom of reducibility for concepts true of only finitely many individuals is still consistent, and that elementary Peano arithmetic (and more) is interpretable in this extended system.     

Basic Infobase Change

Generalisations of theory change involving arbitrary sets of wffs instead of belief sets have become known as base change. In one view, a base should be thought of as providing more structure to its generated belief set, and can be used to determine the theory change operation associated with a base change operation. In this paper we extend a proposal along these lines by Meyer et al. We take an infobase as a finite sequence of wffs, with each element in the sequence being seen as an independently obtained bit of information, and define appropriate infobase change operations. The associated theory change operations satisfy the AGM postulates for theory change. Since an infobase change operation produces a new infobase, it allows for iterated infobase change. We measure iterated infobase change against the postulates proposed by Darwiche et al. and Lehmann.     

The Concept of Truth in a Finite Universe

The prospects and limitations of defining truth in a finite model in the same language whose truth one is considering are thoroughly examined. It is shown that in contradistinction to Tarskirs undefinability theorem for arithmetic, it is in a definite sense possible in this case to define truth in the very language whose truth is in question.     

Some Properties of Orthologics

In this paper, we present three main results on orthologics. Firstly, we give a sufficient condition for an orthologic to have variable separation property and show that the orthomodular logic has this property. Secondly, we show that the class of modular orthologics has an infinite descending chain. Finally we show that there exists a continuum of orthologics.     

Some Remarks on Ultrafilter and Normality Logics

The paper presents the main ideas of Ultrafilter Logic (UL), as introduced by Veloso and others. A new proposal, Normality Logic (NL), is outlined for expanding the expressive power of UL. The system NL appears to offer a simpler solution to the problem of expressive power than the sorting strategy of Carnielli and Veloso. Interpretations of NL are discussed and an important point of contact to Hansson's notion of non-prioritized belief revision is observed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Neglected Ends: Clinical Ethics Consultation and the Prospects for Closure

Clinical ethics consultations (CECs) are sometimes deemed complete at the moment when the consultants make a recommendation. In CECs that involve actual ethical conflict, this view of a consult's endpoint runs the risk of overemphasizing the conflict's resolution at the expense of the consult's process, which can have deleterious effects on the various parties in the conflict. This overly narrow focus on reaching a decision or recommendation in consults that involve profound moral disagreement can result in two types of adverse, lingering sequelae: moral distress or negative moral emotions. The problem, succinctly named, is that such consults have insufficient “closure” for patients, families, and providers. To promote closure, and avoid the ills of moral distress and the moral emotions, I argue that CECs need to prioritize assisted conversation between the different stakeholders in these conflicts, what is often referred to as “bioethics mediation.”     

"In Search of Token Women in Academia": Some Definitions and Clarifications

This article makes an important distinction between two definitions of "token woman." In the first definition, a token woman is one of few women in a predominantly male setting. The second meaning of "Token Woman" identifies that subset of such women who have made the distinctive psychological adaptation described by Laws (1975). The methodological decisions in Young, MacKenzie, and Sherif's (1980) research are justified as based on that definitional distinction. Constantinople's critique is shown to be appropriate as an alternative to Laws' theory, but not as a criticism of our research. Alternative generational explanations for previous findings about Token Women are not supported by existing data.     

On Finite Models of the Lambek Calculus

We study a class of finite models for the Lambek Calculus with additive conjunction and with and without empty antecedents. The class of models enables us to prove the finite model property for each of the above systems, and for some axiomatic extensions of them. This work strengthens the results of [3] where only product-free fragments of these systems are considered. A characteristic feature of this approach is that we do not rely on cut elimination in opposition to e.g. [5], [9].     

Basic Entrenchment

In contrast to other prominent models of belief change, models based on epistemic entrenchment have up to now been applicable only in the context of very strong packages of requirements for belief revision. This paper decomposes the axiomatization of entrenchment into independent modules. Among other things it is shown how belief revision satisfying only the ‘basic’ postulates of Alchourrón, Gärdenfors and Makinson can be represented in terms of entrenchment.     

Contraction: On the Decision-Theoretical Origins of Minimal Change and Entrenchment

We present a decision-theoretically motivated notion of contraction which, we claim, encodes the principles of minimal change and entrenchment. Contraction is seen as an operation whose goal is to minimize loses of informational value. The operation is also compatible with the principle that in contracting A one should preserve the sentences better entrenched than A (when the belief set contains A). Even when the principle of minimal change and the latter motivation for entrenchment figure prominently among the basic intuitions in the works of, among others, Quine and Ullian (1978), Levi (1980, 1991), Harman (1988) and Gärdenfors (1988), formal accounts of belief change (AGM, KM – see Gärdenfors (1988); Katsuno and Mendelzon (1991)) have abandoned both principles (see Rott (2000)). We argue for the principles and we show how to construct a contraction operation, which obeys both. An axiom system is proposed. We also prove that the decision-theoretic notion of contraction can be completely characterized in terms of the given axioms. Proving this type of completeness result is a well-known open problem in the field, whose solution requires employing both decision-theoretical techniques and logical methods recently used in belief change.     

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。