On the Expressive Power of Monotone Natural Language Quantifiers over Finite Models

We study definability in terms of monotone generalized quantifiers satisfying Isomorphism Closure, Conservativity and Extension. Among the quantifiers with the latter three properties – here called CE quantifiers – one finds the interpretations of determiner phrases in natural languages. The property of monotonicity is also linguistically ubiquitous, though some determiners like an even number of are highly non-monotone. They are nevertheless definable in terms of monotone CE quantifiers: we give a necessary and sufficient condition for such definability. We further identify a stronger form of monotonicity, called smoothness, which also has linguistic relevance, and we extend our considerations to smooth quantifiers. The results lead us to propose two tentative universals concerning monotonicity and natural language quantification. The notions involved as well as our proofs are presented using a graphical representation of quantifiers in the so-called number triangle.     

Symmetric Propositions and Logical Quantifiers

Symmetric propositions over domain and signature are characterized following Zermelo, and a correlation of such propositions with logical type- quantifiers over is described. Boolean algebras of symmetric propositions over and Σ are shown to be isomorphic to algebras of logical type- quantifiers over . This last result may provide empirical support for Tarski’s claim that logical terms over fixed domain are all and only those invariant under domain permutations.     

Partially Interpreted Relations and Partially Interpreted Quantifiers

Logics in which a relation R is semantically incomplete in a particular universe E, i.e. the union of the extension of R with its anti-extension does not exhaust the whole universe E, have been studied quite extensively in the last years. (Cf. van Benthem (1985), Blamey (1986), and Langholm (1988), for partial predicate logic; Muskens (1996), for the applications of partial predicates to formal semantics, and Doherty (1996) for applications to modal logic.) This is not so with semantically incomplete generalized quantifiers which constitute the subject of the present paper. The only systematic study of these quantifiers from a purely logical point of view, is, to the best of my knowledge, that by van Eijck (1995). We shall take here a different approach than that of van Eijck and mention some of the abstract properties of the resulting logic. Finally we shall prove that the two approaches are interdefinable.     

Some Closure Properties of Finite Definitions

There is no known syntactic characterization of the class of finite definitions in terms of a set of basic definitions and a set of basic operators under which the class is closed. Furthermore, it is known that the basic propositional operators do not preserve finiteness. In this paper I survey these problems and explore operators that do preserve finiteness. I also show that every definition that uses only unary predicate symbols and equality is bound to be finite.     

Quality and Quantifiers

I examine three ‘anti-object’ metaphysical views: nihilism (there are no objects at all), generalism (reality is ultimately qualitative), and anti-quantificationalism (quantification over objects does not perspicuously represent the world). After setting aside nihilism, I argue that generalists should be anti-quantificationalists. Along the way, I attempt to articulate what a ‘metaphysically perspicuous’ language might even be.     

On the Closure Properties of the Class of Full G-models of a Deductive System

In this paper we consider the structure of the class FGModS of full generalized models of a deductive system S from a universal-algebraic point of view, and the structure of the set of all the full generalized models of S on a fixed algebra A from the lattice-theoretical point of view; this set is represented by the lattice FACS_s A of all algebraic closed-set systems C on A such that (A, C) ε FGModS. We relate some properties of these structures with tipically logical properties of the sentential logic S. The main algebraic properties we consider are the closure of FGModS under substructures and under reduced products, and the property that for any A the lattice FACS_s A is a complete sublattice of the lattice of all algebraic closed-set systems over A. The logical properties are the existence of a fully adequate Gentzen system for S, the Local Deduction Theorem and the Deduction Theorem for S. Some of the results are established for arbitrary deductive systems, while some are found to hold only for deductive systems in more restricted classes like the protoalgebraic or the weakly algebraizable ones. The paper ends with a section on examples and counterexamples. Dedicated to the memory of Willem Johannes Blok     

LÉVY HIERARCHY IN WEAK SET THEORIES

We investigate the interactions of formula complexity in weak set theories with the axioms available there. In particular, we show that swapping bounded and unbounded quantification preserves formula complexity in presence of the axiom of foundation weakened to an arbitrary set base, while it does not if the axiom of foundation is further weakened to a proper class base. More attention is being paid to the necessary axioms employed in the positive results, than to the combinatorial strength of the positive results themselves.     

Processing of Numerical and Proportional Quantifiers

Quantifier expressions like “many” and “at least” are part of a rich repository of words in language representing magnitude information. The role of numerical processing in comprehending quantifiers was studied in a semantic truth value judgment task, asking adults to quickly verify sentences about visual displays using numerical (at least seven, at least thirteen, at most seven, at most thirteen) or proportional (many, few) quantifiers. The visual displays were composed of systematically varied proportions of yellow and blue circles. The results demonstrated that numerical estimation and numerical reference information are fundamental in encoding the meaning of quantifiers in terms of response times and acceptability judgments. However, a difference emerges in the comparison strategies when a fixed external reference numerosity (seven or thirteen) is used for numerical quantifiers, whereas an internal numerical criterion is invoked for proportional quantifiers. Moreover, for both quantifier types, quantifier semantics and its polarity (positive vs. negative) biased the response direction (accept/reject). Overall, our results indicate that quantifier comprehension involves core numerical and lexical semantic properties, demonstrating integrated processing of language and numbers.     

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.”     

Quantifiers and question answering in young children

Two hypotheses were tested about how young children answer questions with the quantifiers all and some: (a) that children use syntactic cues in determining which noun phrase is quantified, and (b) that children evaluate a some-statement as part of evaluating an all-statement. To test these hypotheses, the same group of 60 4- to 7-year-olds were asked four contrasting types of quantitative questions. The results indicated that children can use syntactic cues under some presentation conditions. However, there was no evidence for an asymmetry between the all-and some-questions. A model of how young children might answer quantitative questions was then considered.     

Quantifiers and propositional attitudes: Quine revisited

Quine introduced a famous distinction between the ‘notional’ sense and the ‘relational’ sense of certain attitude verbs. The distinction is both intuitive and sound but is often conflated with another distinction Quine draws between ‘dyadic’ and ‘triadic’ (or higher degree) attitudes. I argue that this conflation is largely responsible for the mistaken view that Quine’s account of attitudes is undermined by the problem of the ‘exportation’ of singular terms within attitude contexts. Quine’s system is also supposed to suffer from the problem of ‘suspended judgement with continued belief’. I argue that this criticism fails to take account of a crucial presupposition of Quine’s about the connection between thought and language. The aim of the paper is to defend the spirit of Quine’s account of attitudes by offering solutions to these two problems. See also chapters four and five of Word and Object (Quine, 1960) and ‘Intensions Revisited’ (Quine, 1977).     

Henkin Quantifiers and the Definability of Truth

Henkin quantifiers have been introduced in Henkin (1961). Walkoe (1970) studied basic model-theoretical properties of an extension L _* ¹(H) of ordinary first-order languages in which every sentence is a first-order sentence prefixed with a Henkin quantifier. In this paper we consider a generalization of Walkoe's languages: we close L _* ¹(H) with respect to Boolean operations, and obtain the language L ¹(H). At the next level, we consider an extension L _* ²(H) of L ¹(H) in which every sentence is an L ¹(H)-sentence prefixed with a Henkin quantifier. We repeat this construction to infinity. Using the (un)-definability of truth – in – N for these languages, we show that this hierarchy does not collapse. In addition, we compare some of the present results to the ones obtained by Kripke (1975), McGee (1991), and Hintikka (1996).     

自立人格与心身症状：特质-应激-症状相符中介模型的检验

自立人格是新近提出的一种新的心身症状的保护性人格因素。为了探索自立人格抵御心身症状的机制, 提出了特质-应激-症状相符中介模型。该模型涉及应激中介模型假设、特质-应激相符假设、特质-症状相符假设三个理论假设。使用青少年学生自立人格量表、青少年生活事件量表和症状自评量表3种问卷对674名有效被试进行了调查, 以检验该模型。结果发现：①应激调节模型不被支持, 自立人格特质是通过应激的中介作用来负向预测心身症状; ②人际自立对心身症状的负向预测能力明显大于个人自立, 人际自立对人际性和个人性症状均有独立的预测能力, 个人自立则对人际性症状没有独立的预测能力; ③个人自立对应激的预测能力大于人际自立, 个人自立对人际和个人应激均有独立的预测能力, 人际自立则对个人应激没有独立的预测能力; ④修正后的自立人格的特质-应激-症状相符中介模型能够获得支持。总之, 本研究的结果显示：人际自立主要通过人际应激的中介作用负向预测心身症状总分; 个人自立则通过应激(包括人际与个人应激)的中介作用负向预测个人性症状。     

Uniform Interpolation and Propositional Quantifiers in Modal Logics

We investigate uniform interpolants in propositional modal logics from the proof-theoretical point of view. Our approach is adopted from Pitts’ proof of uniform interpolationin intuitionistic propositional logic [15]. The method is based on a simulation of certain quantifiers ranging over propositional variables and uses a terminating sequent calculus for which structural rules are admissible. We shall present such a proof of the uniform interpolation theorem for normal modal logics K and T. It provides an explicit algorithm constructing the interpolants. Presented by Heinrich Wansing     

Effects of Psychological Distance and Need for Cognitive Closure on Impression Formation

Based on theoretical and empirical similarities between Construal level theory of psychological distance and the Need for cognitive closure (NFC) theory, it could be hypothesized that psychological distance and NFC represent constructs that overlap to some degree. Since both theories describe judgmental behavior in terms of schematic processing, we hypothesized that primacy effect, a schema-driven phenomenon, is strengthened under the heightened NFC and psychological distance. We tested this hypothesis in an impression formation experiment while manipulating psychological distance and measuring NFC. Low NFC and psychological closeness reflect preference for situationally specific, contextually rich information, and therefore their joint effect resulted in reliance on all available information regardless of their position in a sequence. High NFC and psychological distance produced a preference for clear, schematic, stable knowledge, and therefore weighed first information more, which resulted in the primacy effect.     

积极追随原型-特质匹配对辱虐管理的影响——基于多项式回归与响应面分析的探索

基于内隐追随理论,探索了领导者的积极追随原型(PFP)与追随者的积极追随特质(PFT)之间的匹配程度如何影响辱虐管理。对194份上下级配对数据进行多项式回归和响应面分析,结果显示:(1)相较于非匹配情形,领导者在"PFP—PFT匹配"情形下更少辱虐追随者;(2)与"PFP低—PFT低"相比,"PFP高—PFT高"情形下辱虐管理程度更低;(3)在非匹配情况下,与"PFP高—PFT低"相比,领导者在"PFP低—PFT高"时对追随者有更少的辱虐管理。以上结论能够为组织预防或减少辱虐管理提供理论指导。     

Identifiability and Equivalence of GLLIRM Models

The generalized logit–linear item response model (GLLIRM) is a linearly constrained nominal categories model (NCM) that computes the scale and intercept parameters for categories as a weighted sum of basic parameters. This paper addresses the problems of the identifiability of the basic parameters and the equivalence between different GLLIRM models. It is shown that the identifiability of the basic parameters depends on the size and rank of the coefficient matrix of the linear functions. Moreover, two models are observationally equivalent if the product of the respective coefficient matrices has full column rank. Finally, the paper also explores the relations between the parameters of nested models. I would like to express my gratitude to the editor and three anonymous reviewers for their helpful suggestions on earlier versions of the paper. This work was supported by the Comunidad de Madrid (Spain) grant: CCG07-UAM/ESP-1615.     

Plausible Reasoning and the Resolution of Quantifier Scope Ambiguities

Despite overwhelming evidence suggesting that quantifier scope is a phenomenon that must be treated at the pragmatic level, most computational treatments of scope ambiguities have thus far been a collection of syntactically motivated preference rules. This might be in part due to the prevailing wisdom that a commonsense inferencing strategy would require the storage of and reasoning with a vast amount of background knowledge. In this paper we hope to demonstrate that the challenge in developing a commonsense inferencing strategy is in the discovery of the relevant commonsense data and in a proper formulation of the inferencing strategy itself, and that a massive amount of background knowledge is not always required. In particular, we present a very effective procedure for resolving quantifier scope ambiguities at the pragmatic level using simple quantitative data that is readily available in most database environments.