Complement Anaphora in Spanish: Proportional References and Discourse Relations

Although still disputed by some authors, complement anaphora interpretations are widely accepted today. However, they are marked and subject to strict interpretation conditions. Most commonly, monotone decreasing quantifiers facilitate a salient complement set interpretation that is suitable for subsequent anaphoric reference, whereas monotone increasing quantifiers appear to block such interpretation. In this paper, I investigate the possibilities of anaphoric reference to complement sets in Spanish quantified expressions of type quantifier(A)(B) and argue that Spanish aligns with the general pattern observed cross-linguistically according to which anaphoric reference to the reference set (refset) is default regardless of monotonicity type, and that anaphoric reference to the complement set (compset) is only possible with monotone decreasing quantifiers. My claim is that the observed discrepancy can be explained in terms of the different proportions denoted by the quantifiers, and propose an explanation based on discourse relations. My approach provides additional cross-linguistic evidence in favor of the general observed pattern, and a promising path for future investigation into the refset/compset divide.     

Monotone Quantifiers Emerge via Iterated Learning

Natural languages exhibit many semantic universals, that is, properties of meaning shared across all languages. In this paper, we develop an explanation of one very prominent semantic universal, the monotonicity universal. While the existing work has shown that quantifiers satisfying the monotonicity universal are easier to learn, we provide a more complete explanation by considering the emergence of quantifiers from the perspective of cultural evolution. In particular, we show that quantifiers satisfy the monotonicity universal evolve reliably in an iterated learning paradigm with neural networks as agents.     

The Ambiguity of Quantifiers

In the tradition of substructural logics, it has been claimed for a long time that conjunction and inclusive disjunction are ambiguous:we should, in fact, distinguish between ‘lattice’ connectives (also called additive or extensional) and ‘group’ connectives (also called multiplicative or intensional). We argue that an analogous ambiguity affects the quantifiers. Moreover, we show how such a perspective could yield solutions for two well-known logical puzzles: McGee’s counterexample to modus ponens and the lottery paradox.     

Directions in generalized quantifier theory

We give a condensed survey of recent research on generalized quantifiers in logic, linguistics and computer science, under the following headings: Logical definability and expressive power, Polyadic quantifiers and linguistic definability, Weak semantics and axiomatizability, Computational semantics, Quantifiers in dynamic settings, Quantifiers and modal logic, Proof theory of generalized quantifiers.This paper was inspired by the symposium on Generalized Quantifiers held at the 5th European Summer School in Logic, Language and Information in Lisbon, August 1993. We feel that the work presented there motivates a survey of recent research areas and research problems in the field of generalized quantifiers. The speakers at the symposium, Natasha Alechina, Jaap van der Does, Lauri Hella, Michal Krynicki, Michiel van Lambalgen, Kerkko Luosto, Marcin Mostowski, and Jouko Väänänen, have cooperated and made (oral and/or written) contributions and comments to this research survey which we gratefully acknowledge, and without which it would not have been written. But it is easier to produce a paper with two authors than with ten, and so the present authors take full responsibility for the final formulation of the paper. In addition, we are grateful for comments received from some further colleagues, in particular, Dorit Ben-Shalom, Makoto Kanazawa, Victor Sanchez, Yde Venema and two anonymous referees.Presented byJan Zygmunt     

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。     

扩展三段论的可化归性与广义量词的语义性质之间的关系

基于Barwise、Cooper、Keenan、Peters、Westerstahl和vanEijck等人的研究成果,作者提出并证明了若干事实和推论。这些事实和推论表明：（1）不同三段论之间的可化归性本质上反映了广义量词的单调性、对称性等语义性质之间的可转换性,因此,我们可以根据四个亚氏量词的语义性质之间的转换关系来验证亚氏三段论的可化归性;（2）利用广义量词的语义性质可以验证扩展三段论的不同推理模式之间的可化归关系。由于广义量词在自然语言中普遍存在,因此,本文的研究对广义量词理论的发展和自然语言的信息处理都具有积极意义。     

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).     

阅读理解中汉语量词的眼动特点分析

采用眼动记录技术探讨被试阅读不同汉语量词的即时加工过程。考查名量词和动量词,以及名量词内部的差异。结果发现:(1)被试在阅读理解过程中对名量词和动量词的眼动特点存在显著差异,名量词获得更多的加工;(2)被试在阅读理解过程中对不同名量词的眼动特点也存在显著差异,个体量词比集合量词和临时量词获得更少的加工。由此可知,不同量词在阅读理解中的信息加工难度是不同的,对于篇章理解而言,其信息含量和信息的重要性也是不同的。     

Interpolation and Definability in Guarded Fragments

The guarded fragment (GF) was introduced by Andréka, van Benthem and Németi as a fragment of first order logic which combines a great expressive power with nice, modal behavior. It consists of relational first order formulas whose quantifiers are relativized by atoms in a certain way. Slightly generalizing the admissible relativizations yields the packed fragment (PF). In this paper we investigate interpolation and definability in these fragments. We first show that the interpolation property of first order logic fails in restriction to GF and PF. However, each of these fragments turns out to have an alternative interpolation property that closely resembles the interpolation property usually studied in modal logic. These results are strong enough to entail the Beth definability property for GF and PF. Even better, every guarded or packed finite variable fragment has the Beth property. For interpolation, we characterize exactly which finite variable fragments of GF and PF enjoy this property.     

On modal μ-calculus with explicit interpolants

This paper deals with the extension of Kozen's μ-calculus with the so-called “existential bisimulation quantifier”. By using this quantifier one can express the uniform interpolant of any formula of the μ-calculus. In this work we provide an explicit form for the uniform interpolant of a disjunctive formula and see that it belongs to the same level of the fixpoint alternation hierarchy of the μ-calculus than the original formula. We show that this result cannot be generalized to the whole logic, because the closure of the third level of the hierarchy under the existential bisimulation quantifier is the whole μ-calculus. However, we prove that the first two levels of the hierarchy are closed. We also provide the μ-logic extended with the bisimulation quantifier with a complete calculus.     

Causation as Property Acquisition

Persistence theories of causation – such as transference theory, conserved-quantity theory, and Douglas Ehring's theory – attempt to analyzecausation in terms of some persisting entityconnecting cause and effect. While mostpersistence accounts are intended as empiricaltheories, this article develops a persistenceanalysis of the concept of causation. The basic idea is that the central concept ofdirect causation can be analyzed in terms ofproperty acquisition. The analysis cohereswith our ordinary causal judgments andprovides a straightforward explanation of thedirection of causation. It also explains whybackwards causation is conceptually problematic.     

The nature and varieties of felt presence experiences: A reply to Nielsen

Nielsen [Nielsen, T. (2007). Felt presence: Paranoid delusion or hallucinatory social imagery? Consciousness and Cognition, 16(4), 975–983.] raises a number of issues and presents several provocative arguments worthy of discussion regarding the experience of the felt presence (FP) during sleep paralysis (SP). We consider these issues beginning with the nature of FP and its relation to affective-motivational systems and provide an alternative to Nielsen’s reduction of FP to a purely spatial hallucination. We then consider implications of the “normal social imagery” model. We can find only one specific empirical hypothesis articulated within this framework and it turns out to be one that we explicitly addressed in our original paper. We also review our position regarding the possible relation of FP during SP to a number of related anomalous experiences and contrast FP to anomalous vestibular-motor (V-M) phenomena. We review our position that the neuromatrix concept, in the light of available evidence, is more appropriately applied to V-M experiences than FP. Finally, we pursue speculations, raised in Nielsen’s commentary, on the wider implications of FP.     

Partial monotonicity and a new version of the Ramsey test

We introduce two new belief revision axioms: partial monotonicity and consequence correctness. We show that partial monotonicity is consistent with but independent of the full set of axioms for a Gärdenfors belief revision sytem. In contrast to the Gärdenfors inconsistency results for certain monotonicity principles, we use partial monotonicity to inform a consistent formalization of the Ramsey test within a belief revision system extended by a conditional operator. We take this to be a technical dissolution of the well-known Gärdenfors dilemma.In addition, we present the consequential correctness axiom as a new measure of minimal revision in terms of the deductive core of a proposition whose support we wish to excise. We survey several syntactic and semantic belief revision systems and evaluate them according to both the Gärdenfors axioms and our new axioms. Furthermore, our algebraic characterization of semantic revision systems provides a useful technical device for analysis and comparison, which we illustrate with several new proofs.Finally, we have a new inconsistency result, which is dual to the Gärdenfors inconsistency results. Any elementary belief revision system that is consequentially correct must violate the Gärdenfors axiom of strong boundedness (K^*8), which we characterize as yet another monotonicity condition.This work was supported by the McDonnell Douglas Independent Research and Development program.     

如何利用广义量词的语义性质判断扩展三段论的有效性

在国内外最新研究成果的基础上,笔者通过对文中的定理和推论的证明,主要说明了以下几点：（1）利用广义量词的相关语义性质,比如单调性和对称性,既可以解释亚氏三段论的有效性,又可以解释带有广义量词的扩展三段论的有效性;（2）一些有效的扩展三段论仅仅表征了广义量词的左或右单调性,还有一些有效的扩展三段论同时表征了广义量词的多个语义性质;（3）利用广义量词的东南或西北或西南或东北方向的单调性可以判断一些带有限制条件的扩展三段论的有效性。此研究将有利于广义量词理论的发展,对于计算机科学中的知识表示和知识推理的研究都具有较为重要的理论价值和实践意义。     

How much is ‘quite a bit’? Mapping between numerical values and vague quantifiers

Vague quantifiers, terms like “quite a bit” and “hardly ever”, are often used in the response scales of psychology and social science questionnaires to measure the frequency of certain behaviours. However, responses to such questions arc confounded because people differ in their interpretations of vague quantifiers. We propose that people interpret vague quantifiers by constructing a notion of how most people behave. Examining a critical topic for media researchers–estimating the amount of television walched–we conducted two split-ballot experiments in national surveys. Our first study (n = 1028) demonstrates that the amount people think other people watch varies according to how much television they watch themselves and the behaviour of their social group. Our second experiment (n = 1106) extends this result to the interpretation of vague quantifiers. These findings shed light on the psychological processes involved when interpreting vague quantifiers, and bring into question the validity of many survey results.     

MOST intelligent people are accurate and SOME fast people are intelligent.: Intelligence,working memory,and semantic processing of quantifiers from a computational perspective

The paper explores the relationship between intelligence and the semantic processing of natural language quantifiers. The first study revealed that intelligence is positively associated with the subjects' performance when solving a picture verification task with one of the four types of sentences: Aristotelian (e.g. ‘All cars are red’), parity (e.g. ‘An even number of cars are red’), numerical (e.g. ‘More than five cars are red’), and proportional (‘More than half of the cars are red’). The strongest relationship was observed between the cognitive ability and the accuracy of proportional sentences, in accordance with the computational theory which predicts the highest engagement of working memory (WM) within the group of proportional quantifiers. Moreover, individuals with higher intelligence reacted faster, but this was observed only in case of quantifiers with low complexity. Exploring further, in the second study we found that WM and intelligence were both significant predictors of subjects' score on proportional sentences. In the third study, we examined the relationships between quantifiers, intelligence, short-term memory (STM), and executive control function. STM was correlated with all types of quantifiers that need counting and keeping track of elements (parity, numerical, and proportional). Only proportional quantifiers were associated with cognitive control. The obtained results are discussed within the computational paradigm of language processing.     

Reasoning with quantifiers

In the semantics of natural language, quantification may have received more attention than any other subject, and one of the main topics in psychological studies on deductive reasoning is syllogistic inference, which is just a restricted form of reasoning with quantifiers. But thus far the semantical and psychological enterprises have remained disconnected. This paper aims to show how our understanding of syllogistic reasoning may benefit from semantical research on quantification. I present a very simple logic that pivots on the monotonicity properties of quantified statements--properties that are known to be crucial not only to quantification but to a much wider range of semantical phenomena. This logic is shown to account for the experimental evidence available in the literature as well as for the data from a new experiment with cardinal quantifiers ("at least n" and "at most n"), which cannot be explained by any other theory of syllogistic reasoning.     

Constructivism and the Limits of Reason: Revisiting the Kantian Problematic

The main focus of this paper ison ways in which Kantian philosophy can informproponents and opponents of constructivismalike. Kant was primarily concerned withreconciling natural and moral law. His approachto this general problematic was to limit andseparate what we can know about things(phenomena) from things as they are inthemselves (noumena), and to identify moralagency with the latter. Revisiting the Kantianproblematic helps to address and resolve longstanding epistemological concerns regardingconstructivism as an educational philosophy inrelation to issues of objectivity andsubjectivity, the limits of theoretical andpractical reason, and the relation betweenhuman experience and the world. It also servesto address ethical concerns regardingliberation from limited self-interests andcontexts conditioned by localised beliefs andinclinations. In light of revisiting theKantian problematic, both Glasersfeld's radicalview of constructivism and Jardine's socialcritique of constructivism are found wanting.Beyond constructivism, Kant's distinctionbetween phenomena and noumena and the limits ofreason that follow from it are brieflyconsidered in terms of Merleau-Ponty's noveldouble-embodied notion of flesh as anontological primitive – as a matter of beingboth in, and of, the world – with an aim tomore intimate connections between epistemologyand ethics.     

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).