Universal Quantification Research Articles

Tractable higher-order under-approximating AE extensions for non-linear systems

We consider the problem of under and over-approximating the image of general vector-valued functions over bounded sets, and apply the proposed solution to the estimation of reachable sets of uncertain non-linear discrete-time dynamical systems. Such a combination of under and over-approximations is very valuable for the verification of properties of controlled systems. Over-approximations prove properties correct, while under-approximations can be used for falsification. Coupled, they provide a measure of the conservatism of the analysis. This work introduces a general framework relying on approximations of robust ranges of vector-valued functions, formulated as AE extensions, that can be interpreted as quantified propositions where universal quantifiers (A) precede existential quantifiers (E). This framework allows us to extend for under-approximation many precision refinements that are classically used for over-approximations, such as affine approximations, Taylor models, quadrature formulae and preconditioning methods. We end by evaluating the efficiency and precision of our approach, focusing on the application to the analysis of discrete-time dynamical systems.

Neurolinguistic Programming and English Language Teaching: An Exploration of Linguistic Variants in NLP for its Connection to ELT

The human brain, which can be programmed through a multiplicity of practices, is the foundation of NLP. Language teachers can effectively program their students for improved language output if made aware of the Neuro-functioning of the brain. This new-fangled aspect of language teaching is, hitherto, an uncharted area in the Pakistani teaching context. The current study seeks to look into the existing estate of English language pedagogy in Pakistani scenario with the assistance of the NLP Milton Model, based on the employment of the language patterns by famous hypnotist-Milton Erickson. The focal point of this model is- presupposition, mind read, lost performative, unspecified verb, comparative deletion, cause and effect, universal quantifier, complex equivalence, modal operator, nominalization, and unspecified referential index. It has implications, to a great extent, in ELT to generate preferred results. For this study, the sample population is chosen through purposive sampling technique and encompasses language skills’ classes; whereas, the five English Language institutions were preferred through random sampling method. This study, accordingly, underpins the exploitation of NLP as a toolkit for effectual language pedagogy. Besides, it also advocates copious ways for meaningful, motivational, and momentous communication between language teachers and learners.

Türkçede olumsuzluğa duyarlı ifadeler: Olumsuz uçluk mu olumsuz uyum mu?

This paper is concerned with the nature of negative sensitive items such as hiçkimse ‘no one’ and asla ‘never’ in Turkish. It is well attested in previous studies that these negative sensitive elements require the obligatory presence of sentential negation or some other licensor in the structure. However, there is still an ongoing controversy as to what these negative sensitive elements actually are and why they behave the way they do. Some researchers proposed that these elements are negative polarity items (NPIs) whereas others suggested that they are (existential) n-words or negative concord items (NCIs). Therefore, the question remains as to which category these elements belong to in the language. In this work, I address this question by using a comprehensive set of diagnostic tests proposed in prior work to find out the true characteristic of these elements. I argue that their syntactic and semantic behavior strongly indicate that they should be classified as NCIs, and not as NPIs in Turkish. I also show that these negative sensitive items display the characteristics of both the universal quantifier and the existential quantifier. This is because they can be interpreted either way in the language. This finding is compatible with the cross-linguistic predictions that NCIs are able to display the behavior of different quantificational elements across languages.

The nature of the semantic stimulus: the acquisition of every as a case study

We evaluate the richness of the child’s input in semantics and its relation to the hypothesis space available to the child. Our case study is the acquisition of the universal quantifier every. We report two main findings regarding the acquisition of every on the basis of a corpus study of child-directed and child-ambient speech. Our first finding is that the input in semantics (as opposed to the input in syntax or phonology) is rich enough to systematically eliminate instances of the subset problem of language acquisition: overly general hypotheses about the meaning of every can violate pragmatic constraints, making such hypotheses incompatible with the child’s input. Our second finding is that the semantic input is too poor to eliminate instances of what we refer to as the superset problem, the mirror image of the subset problem. We argue that at least some overly specific hypotheses about the meaning of every are compatible with the child’s input, suggesting either that those hypotheses are not made available by UG or that non-trivial inductive biases are involved in children’s acquisition of every.

Quantum B-algebras with involutions

The aim of this paper is to define and study the involutive and weakly involutive quantum B-algebras. We prove that any weakly involutive quantum B-algebra is a residuated poset. As an application, we introduce and investigate the notions of existential and universal quantifiers on involutive quantum B-algebras. It is proved that there is a one-to-one correspondence between the quantifiers on weakly involutive quantum B-algebras. One of the main results consists of proving that any pair of quantifiers is a monadic operator on weakly involutive quantum B-algebras. We investigate the relationship between quantifiers on bounded sup-commutative pseudo BCK-algebras and quantifiers on other related algebraic structures, such as pseudo MV-algebras and bounded Wajsberg hoops.

Comparisons of Equality With Germanso…wie, and the Relationship Between Degrees and Properties

AbstractWe present a compositionally transparent, unified semantic analysis of two kinds of so…wie-equative constructions in German, namely degree equatives and property equatives in the domain of individuals or events. Unlike in English and many other European languages (Haspelmath & Buchholz 1998, Rett 2013), both equative types in German feature the parameter marker so, suggesting a unified analysis. We show that the parallel formal expression of German degree and property equatives is accompanied by a parallel syntactic distribution (in predicative, attributive, and adverbial position), and by identical semantic properties: Both equative types allow for scope ambiguities, show negative island effects out of context, and license the negative polarity item überhaupt ‘at all’ in the complement clause. As the same properties are also shared by German comparatives, we adopt the influential quantificational analysis of comparatives in von Stechow (1984ab), Heim (1985, 2001, 2007), and Beck (2011), and treat both German equative types in a uniform manner as expressing universal quantification over sets of degrees or over sets of properties (of individuals or events). Conceptually, the uniform marking of degree-related and property-related meanings is expected given that the abstract semantic category degree (type $d$) can be reconstructed in terms of equivalence classes, i.e., ontologically simpler sets of individuals (type $\langle e,t\rangle $) or events (type $\langle v,t\rangle $). These are found in any language, showing that whether or not a language makes explicit reference to degrees (by means of gradable adjectives, degree question words, degree-only equatives) does not follow on general conceptual or semantic grounds, but is determined by the grammar of that language.

Domain restriction in child Mandarin: Implications for quantifier spreading

AbstractThis study explores Mandarin children’s competence with quantifier domain restriction. We present results from two experiments in which adults and four- to five-year old children evaluated two possible candidates for the domain selection associated with the distributive operatordou‘all’ in Mandarin Chinese. In the first experiment, we investigated whether children and adults are capable of selecting an appropriate domain when two candidate NPs both appear insidedou’s quantification scope; i.e., both of the NPs c-commanddou. In the second experiment, still two candidate NPs were presented, but one withindou’s scope and the other outside its scope. Our results indicate that four- to five-year-old children are capable of basic distributive computation associated withdou, but they may choose an NP that adults do not usually choose as the domain ofdou, resulting in non-adult interpretations of distributive computation in certain cases. Based on the results, we propose that four- to five-year-old children are less certain about the domain restriction associated withdou-quantification. This proposal has important implications for the current debate on the acquisition of universal quantifiers, specifically, the problem of quantifier spreading. We explain children’s uncertainty about the domain restriction with a universal grammar-based statistical acquisition model.

Event-distributivity and exhaustivity

Abstract Distributive-share markers such as jeweils in German or po in Serbian allow for event-distributive readings, where events are distributed over spatio-temporal units, unlike distributive quantifiers such as each in English that only allow individual-distributive readings. Some researchers propose that German jeweils should be analyzed as a universal event-distributive quantifier. In contrast, other researchers claim distributive share markers (e.g. Serbian po) are simply event plurality markers. We investigated these claims with jeweils in two experiments. Experiment 1 tested if both individual and spatial (event) distributive readings are readily available for transitive sentences in German, and if there is an exhaustivity requirement on the restrictor argument. Experiment 2 was designed to force event-distributive readings and further disambiguate the results from Experiment 1. Our findings suggest that jeweils seems to be a true universal event quantifier, and highlight that distributive share markers can differ in fundamental features cross-linguistically.

All good and well

Abstract The Dutch expression goed en wel ‘good and well’ is polysemous. In one of its uses, goed en wel combines with a universal quantifier alles or allemaal ‘all’ and the conjunction maar ‘but’. The resulting construction is typically used to introduce a contrary reaction to an earlier utterance or suggestion. The combination is shown to fit into a larger class of pragmatic operators, which are argued to be instances of lexicalized pragmatics.

Intonational effects on English scopally-ambiguous sentences

This paper examines the effect of intonation contour on two types of scopally ambiguous constructions in English: configurations with a universal quantifier in subject position and sentential negation (e.g., Every horse didn’t jump) and configurations with quantifiers in both subject and object positions (e.g., A girl saw every boy). There is much prior literature on the relationship between the fall-rise intonation and availability of inverse scope with quantifier-negation configurations. The present study has two objectives: (1) to examine whether the role of intonation in facilitating inverse scope is restricted to this configuration, or whether it extends to double-quantifier configurations as well; and (2) to examine whether fall-rise intonation fully disambiguates the sentence, or only facilitates inverse scope. These questions were investigated experimentally, via an auditory acceptability judgment task, in which native English speakers rated the acceptability of auditorily presented sentences in contexts matching surface-scope vs. inverse-scope readings. The results provide evidence that fall-rise intonation facilitates the inverse-scope readings of English quantifier-negation configurations (supporting findings from prior literature), but not those of double-quantifier configurations.

GRAMATICALIZAÇÃO DE GERAL NO PORTUGUÊS BRASILEIRO

A gramaticalização é um processo que desenvolve formas gramaticais a partir de formas lexicais e formas ainda mais gramaticais a partir de formas já gramaticais (KURYŁOWICZ, 1975[1965]; HOPPER; TRAUGOTT, 2003; HEINE; KUTEVA, 2005, entre outros). Este trabalho descreve o processo de gramaticalização pelo qual está passando o adjetivo geral na língua portuguesa. A partir da análise de dados extraídos do Corpus do Português (DAVIES; FERREIRA, 2006) e da rede social Twitter, propõe-se que esse adjetivo é empregado com valor adverbial em alguns contextos nos quais determina o verbo e como um quantificador universal em contextos nos quais satura o predicador verbal, seja na posição de sujeito seja na de objeto. As evidências que atestam o processo de gramaticalização deste adjetivo incluem (i) a extensão, pois ele passa a ocorrer em ambientes onde anteriormente não ocorria; (ii) a dessemantização, já que ele passa a veicular um sentido gramatical, sobretudo em seu uso como quantificador, equivalendo ao sentido do pronome indefinido todos; e (iii) a descategorização, uma vez que, em contextos onde é usado em sua forma gramaticalizada, perde a propriedade de se flexionar em número. O cline de gramaticalização proposto segue a direção de adjetivo > substantivo > advérbio > pronome indefinido/quantificador.

Negative Polarity in ‮כל‬‎ Constructions in Qumran Hebrew

Abstract The Hebrew quantifier ‮כל‬‎ is used both as a universal quantifier (equivalent to English all) and as a distributive quantifier (equivalent to English each, every). In Qumran Hebrew, as in Biblical Hebrew, the quantifier ‮כל‬‎ occurs in four syntactic constructions depending upon the type of noun phrase that follows it in order to indicate nuances of individuation and specificity in addition to universal and distributive quantification. In contexts in which these constructions occur within the scope of negation, the quantifier assumes negative polarity (none, nothing, any in English). In this article, we identify the syntactic contexts and constructions in which negative polarity is licensed and we describe and analyze the constructions of ‮כל‬‎ with negative polarity. We also compare the negative polarity licensing exhibited in Qumran Hebrew with Biblical Hebrew and demonstrate that some of the features of negative polarity in Qumran Hebrew differ from those in Biblical Hebrew.

Founded semantics and constraint semantics of logic rules

Abstract Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs, including in attempting to solve the well-known Russell’s paradox. These semantics are often non-intuitive and hard-to-understand when unrestricted negation is used in recursion. This paper describes a simple new semantics for logic rules, founded semantics, and its straightforward extension to another simple new semantics, constraint semantics, that unify the core of different prior semantics. The new semantics support unrestricted negation, as well as unrestricted existential and universal quantifications. They are uniquely expressive and intuitive by allowing assumptions about the predicates, rules and reasoning to be specified explicitly, as simple and precise binary choices. They are completely declarative and relate cleanly to prior semantics. In addition, founded semantics can be computed in linear time in the size of the ground program.

Morphosyntactic Cues for Quantifier Comprehension in Children

ABSTRACT Universal quantifiers, which refer to groups of individuals or events, can express a subtle distinction between collective (unified or simultaneous) and distributive (individuated and separate) events. Indeed, English uses different quantifiers for this distinction (“all” and “each”, respectively). Hebrew, however, has a single universal quantifier. Thus, the collective/distributive distinction associated with the universal quantifier is represented morphosyntactically. This study examined whether Hebrew-speaking children (4–6 year olds) detect the collective/distributive distinction based on morphosyntactic cues alone and whether they show similar performance pattern as adults. Using a novel drawing task, instructions were given in either a collective-preferred form or a distributive form, asking participants to add drawings to pictures of multiple items. Within-subjects (Experiment 1) and between-subjects designs (Experiment 2) were used. Overall, children distinguished between the forms, indicating that they attended the specific morphosyntic cues of these two forms. They produced distributive drawings following the distributive form, similarly to adults. However, they alternated between distributive and collective drawings following the collective-preferred form, unlike adults who mostly gave collective responses. We discuss a possibility for the interplay between the meaning of the universal quantifier and the morphosyntactic cues in children’s performance. This study provides insights into the acquisition of meaning that depends on morphosyntax.

Indeterminate pronouns in Old English: a compositional semantic analysis

Indeterminate pronouns in Old English (expressions like hwa ‘who/what’ and hwelc ‘which’) permit several interpretations in addition to their use as interrogative pronouns, for example readings as universal or existential quantifiers. They combine with morphological prefixes (ge- ‘and, also’ and a- ‘always, ever’), which change the range of possible interpretations. Old English indeterminate pronouns are shown to contribute a crosslinguistically hitherto unattested pattern of available interpretations. In particular, bare indeterminate pronouns have a universal interpretation and ge-indeterminate pronouns can be both universal and existential. This paper offers an alternative semantic analysis in the spirit of Hamblin (Found Lang 10:41–53, 1973) and Shimoyama (Nat Lang Semant 14:139–173, 2006). A compositional semantics is given for the pronouns and the prefixes, which derives the available readings. The paper ends with a proposal for compositional semantic change relating Old English indeterminate pronouns to their modern descendants.

Monadic pseudo BE-algebras

Abstract In this paper we define the monadic pseudo BE-algebras and investigate their properties. We prove that the existential and universal quantifiers of a monadic pseudo BE-algebra form a residuated pair. Special properties are studied for the particular case of monadic bounded commutative pseudo BE-algebras. Monadic classes of pseudo BE-algebras are investigated and it is proved that the quantifiers on bounded commutative pseudo BE-algebras are also quantifiers on the corresponding pseudo MV-algebras. The monadic deductive systems and monadic congruences of monadic pseudo BE-algebras are defined and their properties are studied. It is proved that, in the case of a monadic distributive commutative pseudo BE-algebra there is a one-to-one correspondence between monadic congruences and monadic deductive systems, and the monadic quotient pseudo BE-algebra algebra is also defined.

Dancing monkeys in Serbian and Korean – exhaustivity requirements on distributive share markers

In some languages, distributive markers/quantifiers can attach to the argument that is being distributed (the distributive share), as opposed to the restrictor of the sentence (the distributive key). Researchers agree that distributive share markers can also distribute over events (and not only individuals), but disagree as to what these markers are semantically – universal distributive quantifiers or event plurality (pluractional) markers. In this paper, we experimentally probe spatial event distribution. On a universal quantification account, exhaustive distribution over a spatial distributive key is enforced, while on the pluractional analysis there is no such requirement. We carried out two picture verification experiments to test exhaustivity requirements in intransitive sentences with distributive share markers from two typologically different languages: the Serbian marker po and the Korean marker -ssik. We found evidence for an exhaustivity requirement over pluralities of non-atomic individuals (groups), but not over designated spatial locations. We interpret these findings as evidence that the semantics of (spatial) event distribution with distributive share markers involves a (spatial) distributive key. Specifically, po/-ssik have a universal quantificational force (with a meaning akin to per (each)) establishing a distributive relation between individual events and elements of the spatial distributive key. Plural individuals made salient in the visual input can serve to divide up the spatial key into chunks of space that have to be exhausted.

Homogeneity and universal quantification in embedded questions

Based on experiments carried out in three languages (German, Dutch, Ulster English) we provide evidence for the claims that question-internal universal quantifiers (who all) can be made at-issue and collapse homogeneity in embedded contexts. We show that these question quantifying particles can be accounted for in a domain restriction analysis (Brisson, 2003). Couched within the account of homogeneity provided in Kriz and Spector (2020), homogeneity removal follows as a result of these particles flattening the alternatives which enter into the computation of homogeneity.

Quantitative speciation of volatile sulphur compounds from human cadavers by GC-ICP-MS

This work demonstrates the first forensic application of GC-ICP-MS for improved investigations of volatile organic compounds originating from a decomposing body. Volatile organic compounds were extracted from the headspace of human remains using sorbent tubes over a total time of 39 days. To account for naturally abundant species, control sites were prepared and sampled accordingly. All samples were spiked with an internal standard to minimise drift effects and errors during sample preparation and further analysis. Compound independent quantification was possible from a single chromatogram with a standard mix containing volatile pesticide compounds representing different mass fractions of target elements for calibration. Phosphorus, sulphur and chlorine were investigated as biologically relevant elements, which potentially form detectable volatile species during decomposition. The limits of detection of these elements in the headspace were 0.7, 5.4 and 1.6 ng/L, respectively. For sulphur, we identified abundant species which increased in concentrations of up to 1310 ng/L in the headspace above the remains. The concentrations were time dependent and show potential as forensic markers to determine post-mortem intervals or decomposition states. The universal quantification, standardisation and the high sensitivity of GC-ICP-MS augments traditional GC-MS analyses.

Epistemic Future and epistemic modal verbs in Portuguese

This paper discusses the semantics of two epistemic operators in Portuguese: the epistemic Future and modal verbs. The idea sustained in the literature for other languages that the epistemic Future has the same semantics as the modal verb (equivalent to) MUST does not account for the Portuguese data. The proposal is made that, though epistemic Future and epistemic modal verbs are devices to convey uncertainty, they operate on different grounds. Epistemic modal verbs are quantifiers over possible worlds, expressing a degree of epistemic commitment towards a proposition, while the epistemic Future is argued to be a mark signaling lack of evidence at the context of utterance. The other modal verbs of Portuguese, in their epistemic reading, are also considered, the proposal being made that Portuguese has also a modal verb that existentially quantifies over the set of Best worlds. This shows a very symmetric picture of Portuguese modal verbs: two of them select an ordered modal base and two others an unordered modal base; for each domain of quantification – the entire modal base or the set of Best Worlds (a subset of the modal base) – there will be an existential and a universal quantifier.