Universal Quantification Research Articles

Negative Dependencies in Turkish

In this paper, we provide an overview of negative dependencies in Turkish. The first are elements such as hiçkimse, which sometimes seem to mean ‘anybody’ and sometimes ‘nobody’. We argue that unlike a standard Negative Polarity Item (NPI) like English anybody, these items should be analyzed as neg-words licensed under Negative Concord (NC). We also discuss further properties of these items, including whether they are universals or existentials. The second set of items that display a negative dependency are universal quantifiers such as herkes ‘everybody’. Unlike their counterparts in many languages, these items obligatorily scope under negation, which raises the question of why a universal is sensitive to negation in the way it is. We account for this behavior in terms of negative polarity sensitivity based on a referentiality requirement we dub the Non-Entailment-of-Non-Existence Condition, following a particular analysis of a class of NPIs in Mandarin. The final case of negative dependency we evaluate is modals that have to scope under or above negation. These cases constitute instances of polarity sensitivity in English and beyond, especially clearly in the case of modal PPIs. We show that in Turkish, however, they do not, and the apparent negative dependency follows from the syntax of Tense-aspect-modality (TAM) morphology.

Quantifiers in connexive logic (in general and in particular)

Abstract Connexive logic has room for two pairs of universal and particular quantifiers: one pair, $\forall $ and $\exists $, are standard quantifiers; the other pair, $\mathbb{A}$ and $\mathbb{E}$, are unorthodox, but we argue, are well-motivated in the context of connexive logic. Both non-standard quantifiers have been introduced previously, but in the context of connexive logic they have a natural semantic and proof-theoretic place, and plausible natural language readings. The results are logics that are negation inconsistent but non-trivial.

An Argument for a Strong Force Semantics of Believe

Abstract The English verb believe is usually taken to encode universal quantification over possibilities (Hintikka 1969) and thus it is predicted to carry a strong modal force. Faced with the intuition that believe feels weaker than uncontroversially strong modals like sure, Hawthorne et al. (2016) instead propose that believe carries a weak modal force, requiring that the agent’s degree of certainty exceed some vague standard and drawing a parallel to relative gradable adjectives like tall. The current contribution takes to heart the idea that believe is gradable but shows that its scale properties in fact argue against a weak force semantics: the scale of believe is upper-closed and so its default standard must be the scale maximum (Kennedy and McNally 2005; Kennedy 2007). This results in a strong modal force, suggesting that the felt weakness of believe is rooted in its ‘subjective’ modal flavor (cf. Lyons 1977; Kratzer 1981) arising from the fact that believe maps propositions to degrees of credence.

Russian Disjunction To li To li and Obligatory Ignorance

Abstract In this paper, we explore the behavior of one complex disjunction in Russian that has some special properties that set it apart from other simple and complex disjunctions: it never gives rise to free choice inferences in environments in which other disjunctions do and under universal quantifiers it behaves different from other disjunctions. We show that the data resist an analysis in terms of wide scope disjunction and propose that those special properties are due to obligatory ignorance inferences associated with this disjunction. The paper provides one more argument for a grammatical theory of ignorance along the lines of ( 7).

Cultural Transitions in Mathematical Discourse: Unveiling Mathematical Writing Hurdles during the Rite of Passage

This qualitative case study delves into the intricate landscape of mathematical writing challenges faced by first-year university students undergoing the critical transition from school-level to university-level mathematical discourse. Conducted at a prominent South African university, the research, employing a purposive sampling technique, engaged thirty first-year mathematics students. Guided by the community of practice theory by Lave and Wenger, alongside van Gennep’s rite of passage analytical lens, the study sought answers to the question: What are the mathematical writing challenges encountered by first-year university students during their rite of passage period? Thematic analysis, informed by Adu's (2019) coding framework, was utilized to systematically examine common themes and patterns within the qualitative data. The findings illuminated key hurdles during this transitional phase, prominently including the inconsistency in working with mathematical notations, erroneous use of universal and existential quantifiers, and a notable confusion between the acts of illustrating and proving in mathematical contexts. In response to these challenges, the study advocates for the explicit incorporation of mathematical writing instruction to scaffold students during this rite of passage. Furthermore, it recommends a shift in the emphasis of first-year mathematics courses—suggesting a redirection from a content-centric approach to one that prioritizes the cultivation of students' new identities. This entails focused attention on teaching the customs, traditions, and adept ways of constructing and articulating mathematical proofs in the university context. The implications of this study extend beyond the immediate challenges identified, offering actionable recommendations to enhance the pedagogical strategies employed in the crucial transition period for first-year mathematics students.

HYPNOINDUCTORS OF THE EFFECTIVE FORMULA OF POSITIVATION IN SOCIAL ADVERTISING DISCOURSE

The article is devoted to influential elements of social advertising discourse, where Milton-model inductions are arranged, which is proposed to be nominated as hypnoinducers. The purpose of the study was to identify actual hypnoinducers of the influential formula of positivity in social advertising discourse. The object of intelligence research is Ukrainian advertising megadiscourse, the subject is suggestive markers of Ukrainian social advertising discourse. General scientific methods contributed to the delineation of specific features of social advertising discourse, various types of hypnoinducers (descriptive method); identification of the components of a communicative suggestion and combining them into a whole (methods of analysis and synthesis); concretization of general conclusions (method of induction); construction of formula models of advertising influence (modeling method). Special linguistic — the study of the semantic load and functional features of linguistic components of social advertising discourse (contextualinterpretive and component analysis) and the communicative nature of advertising suggestogens (elements of discursive analysis). The methodological base of the latest scientific directions (suggestive linguistics and neurolinguistic programming) made it possible to differentiate and systematize relevant markers (hypnoinducers) of advertising suggestion (methods of meta- and Milton-model identification and suggestive qualification, which are distinguished by R. Bandler, J. Grinder, M. Erikson, T. Yu. Kovalevska. The formulas of vectors of emotional orientation of influence are presented: positivity, negation and change of vector (in commercial, political and social advertising discourses), where special attention is paid to the formula of positivity realized in social advertising discourse. Relevant hypnoinducers, which are fixed in the above formula. In particular, hypnoinducers of complex syntactic structure + lexical-semantic hypnoinductors ("point" markers) and actually lexical-semantic hypnoinducers are singled out. Truisms can act as hypnoinducers of complex syntactic structure; pattern break; "reading thoughts" complicated by other hypnoinducers, and quotations, or "quotes" of an established and transformed structure, which, in turn, often act as separate hypnoinducers without the support of lexical and semantic markers. Elements of the inverse metamodel of the processes of omission (nominalization, nonspecific vocabulary) and generalization (universal quantifiers, modal operators of necessity) act as lexical-semantic hypnoinducers. The characteristic feature is the presence of affectives as super (powerful) hypnoinducers, the presence of ergonomics varies, and predicates are not clearly represented. Prospects for research development: in-depth analysis and systematization of current hypnoinducers in various genres of advertising discourse, which will expand the spectrum of the most effective influential dominants.

Two Varieties of Korean: Rightward Head Movement or Polarity Sensitivity?

A strong argument in favor of the existence of rightward, string-adjacent head movement comes from Han, Lidz, and Musolino (2007). They argue that Korean language-internal variation with respect to the scopal order between negation and universal quantifier objects shows that in the variety where negation takes wide scope, the negative marker must have moved along with the verb/auxiliary to the head of IP. This would then constitute evidence for rightward, string-adjacent head movement. In this article, I argue that this analysis actually makes different predictions than have been attested in Korean. Moreover, I argue that, following a well-known stand with respect to the nature of polarity sensitivity (Chierchia 2013), these facts follow naturally once it is assumed that in one variety, but not the other, universal quantifiers are positive polarity items. This makes the attested language-internal variation in Korean less exceptional since language-internal variation with respect to polarity sensitivity is widely attested.

An experimental study of classical truth logic on multi-propositions consistent and incompatible: Dual-process theories and modal syllogistic of deduction.

This study looked at a classical truth logic of multi-propositions that is new in some ways: [1] Alethic modalities were mixed with logical consistency and incompatibility in a single plate form, i.e., necessary consistency (NC), possible consistency (PC)/ possible incompatibility (PI) and impossible incompatibility (IPI); [2] multi-propositions were judged by individuals as either NC, PC/PI, or IPI; [3] Four quantifiers; All (∀), No (∼∀), Some (∃), and Some Not (∼∃) of four propositional modes and three shapes ([Formula: see text], ▱ and [Formula: see text]) are used to evaluate predictions; and [4] it inspired by multi-propositional of dual-process theories (DPTs) of deduction and modal syllogistic of multi-propositions, from which logicians have derived general hypotheses. HP 1- Individuals will more likely to endorse inferences as PC/PI rather than NC. HP 2: It's easier to calculate that inference has PC/ PI if it has also NC. Generally, logicians predict more endorsing PC for NC than for PI proposition. HP 3: It's easier to calculate that inference is not NC if it is also not PC. Generally, logicians predict more PI than IPI proposition endorses as NC. A modal syllogistic as a classical truth logic is presented by multi-propositions (two premises and one inference), each one from four modes has quantifiers such as universal quantifiers and existential quantifier; ∀, ∼∀, ∃, and ∼ ∃. They were evaluated by a single-mental model (Experiment I) and a multi-mental model (Experiment II). Logicians applied the immediate inference task (IIT), evaluation task (ET), and production task (PT) to evaluate three experiments. The results of the experiments suggested that students mostly endorsed PC/PI inferences over NC inferences. Even when logicians divided PC/PI separately as PC and PI, individuals endorsed PC most likely as compared to NC, and PI than IPI. Logicians also highlighted fallacies that were continuously resisted and endorsed when students were asked to judge multi-propositions that had NC. The purpose of this experimental study is to present a glimpse of students' endorsement of multi-propositions and explain that each individual has a different working memory and intelligence.

Negative concord in fragments: Reexamining the evidence against the negativity of negation markers

I argue that particular restrictions on the recoverability of elided negation in fragment answers in negative-concord languages follow from the semantics of questions. Drawing parallels with other ellipsis phenomena, I also highlight the role of Agree in making certain heads recoverable. This invalidates a major argument against the analysis of negative-concord items as universal quantifiers scoping above negation.

Transpension: The Right Adjoint to the Pi-type

Presheaf models of dependent type theory have been successfully applied to model HoTT, parametricity, and directed, guarded and nominal type theory. There has been considerable interest in internalizing aspects of these presheaf models, either to make the resulting language more expressive, or in order to carry out further reasoning internally, allowing greater abstraction and sometimes automated verification. While the constructions of presheaf models largely follow a common pattern, approaches towards internalization do not. Throughout the literature, various internal presheaf operators ($\surd$, $\Phi/\mathsf{extent}$, $\Psi/\mathsf{Gel}$, $\mathsf{Glue}$, $\mathsf{Weld}$, $\mathsf{mill}$, the strictness axiom and locally fresh names) can be found and little is known about their relative expressivenes. Moreover, some of these require that variables whose type is a shape (representable presheaf, e.g. an interval) be used affinely. We propose a novel type former, the transpension type, which is right adjoint to universal quantification over a shape. Its structure resembles a dependent version of the suspension type in HoTT. We give general typing rules and a presheaf semantics in terms of base category functors dubbed multipliers. Structural rules for shape variables and certain aspects of the transpension type depend on characteristics of the multiplier. We demonstrate how the transpension type and the strictness axiom can be combined to implement all and improve some of the aforementioned internalization operators (without formal claim in the case of locally fresh names).

Numerical expressive power of logical languages with cardinality comparison

Abstract In this paper, we investigate the numerical expressive power of various logical languages, encompassing fragments of Presburger Arithmetic (PbA), monadic second-order logic with counting with respect to finite domains (MSO$^{\phi }(\#)$) and shallow second-order graded modal logic with counting with respect to image-finite frames (SOGML$^{\textsf{s},\phi }$(#)). We show that in their respective existential fragments, the $1$-free fragment of PbA, the =-free fragment of MSO$^{\phi }(\#)$ and the graded modality-free fragment of SOGML$^{\textsf{s},\phi }$(#) possess equivalent numerical expressive power, specifically defining strongly semilinear sets. When adding universal quantifiers or adding $1$, = and graded modality to these three languages, the resulting definable sets become semilinear sets.

Wh-Words: Existential or Universal Quantifiers in Child Mandarin?

Wh-words have been analysed as existential quantifiers (Chierchia in Logic in grammar: polarity, free choice, and intervention. Oxford University Press, Oxford, 2013; Fox, in Sauerland U, Stateva P (eds) Presupposition and implicature in compositional semantics (Palgrave studies in pragmatics, language and cognition). Palgrave MacMillan, Houndmills, pp 71-120, 2007; Liao in Alternative and exhaustification: non-interrogative uses of Chinese wh-words. Harvard University, 2010) or universal quantifiers (Nishigauchi, in: Theoretical and applied linguistics at Kobe Shoin 2, Kobe Shoin Institute for Linguistic Sciences, 1999). These two accounts have distinct predictions on how children initially interpret wh-words. The universal account predicts that children should initially interpret wh-words as universal quantifiers, whereas the existential account anticipates that children should start out with the existential interpretation. To adjudicate between the two accounts, the present study was designed to explore pre-schoolers' semantic knowledge of wh-quantification. Specifically, it investigated the interpretation of the wh-word shenme 'what' with 4-and 5-year-old Mandarin-speaking children and a control group of adults. Using a Truth Value Judgment Task (Crain and Thornton in Investigations in universal grammar: a guide to experiments on the acquisition of syntax and semantics. MIT Press, Cambridge, 1998), Experiment 1 evaluated whether children interpret the wh-word shenme 'what' as closer in meaning to the polarity sensitive item renhe 'any' or the universal quantifier suoyou 'all' in the antecedent of ruguo 'if' conditionals. Using a Question-Answer Task, Experiments 2 & 3 respectively investigated whether children interpret shenme 'what' as closer in meaning to renhe 'any' or suoyou 'all' in two types of questions: yes-no questions with the particle ma and A-not-A questions. It was found that both children and adults interpret shenme 'what' as closer in meaning to renhe 'any' than suoyou 'all'. The findings suggest that Mandarin-speaking pre-schoolers already have adult-like semantic knowledge of wh-quantification: wh-words are existential quantifiers rather than universal quantifiers. Due to the paucity of primary linguistic input, children's early mastery of the non-interrogative wh-words appear to support the biolinguistic approach to language acquisition (Chomsky in Aspects of the theory of syntax. MIT Press, Cambridge, 1965; Pinker in Language learnability and language development. Harvard University Press, Cambridge, 1984; Crain et al. in Language acquisition from a biolinguistic perspective. Neurosci Biobehav Rev, 2016. https://doi.org/10.1016/j.neubiorev.2016.09.004 ).

Cross-linguistic comparisons on distributive universal quantification: <i>Each</i> vs. <i>every</i> vs. <i>mei</i>

This paper discusses differences between each and every with regard to (a) pair-list readings; (b) subject/object asymmetries seen with every but not with each; and (c) the long-held intuition that each is more individualistic whereas every is friendlier to groups. We propose that these phenomena can be captured by prior accounts of the Mandarin Chinese distributive universal quantifier mei. In particular, we consider the Double Variable Hypothesis (the idea that in DUQ, for every x, there must be a y) (S.-Z. Huang 1995; 1996), and the Skolemized Topicality Hypothesis (the idea that topical quantifiers are Skolemized, resulting in the required x-y pairings) (S.-Z. Huang 2022b). We argue that (a’) pair-list answers to questions with quantifiers are derivable from the Double Variable Hypothesis; (b’) the subject/object asymmetry seen in every is due to its positionally-varied association with the Double Variable Hypothesis, while each is always subject to Skolemized Topicality due to its inherent topicality; and (c’) the individualistic interpretation of each can be described as stemming from its intrinsically Skolemized topicality as well. Results from experimental works will be brought to bear on the theoretical proposals.

Characterising Context-Independent Quantifiers and Inferences

Abstract Context is essential in virtually all human activities. Yet some logical notions seem to be context-free. For example, the nature of the universal quantifier, the very meaning of “all”, seems to be independent of the context. At the same time, there are many quantifier expressions, and some are context-independent, while others are not. Similarly, purely logical consequence seems to be context-independent. Yet often we encounter strong inferences, good enough for practical purposes, but not valid. The two types of examples suggest a general problem: how to characterise the context-free logical concepts in their natural environment, that is, in the field of their context-dependent associates. A general Thesis on Quantifiers is formulated: among all quantifiers, the context-free ones are just those definable by the universal quantifier. The issue of inferences is treated following the approach introduced by Richard L. Epstein: valid ones are an extreme case, the result of the disappearance of context-dependence. This idea can be applied to an analysis of a form of abduction, called “reductive inference” in Polish literature on logic. A tentative Thesis on Inferences identifies the validity of a strong inference that is context-independent.

ONE-VARIABLE FRAGMENTS OF FIRST-ORDER LOGICS

AbstractThe one-variable fragment of a first-order logic may be viewed as an “S5-like” modal logic, where the universal and existential quantifiers are replaced by box and diamond modalities, respectively. Axiomatizations of these modal logics have been obtained for special cases—notably, the modal counterparts $\mathrm {S5}$ and $\mathrm {MIPC}$ of the one-variable fragments of first-order classical logic and first-order intuitionistic logic, respectively—but a general approach, extending beyond first-order intermediate logics, has been lacking. To this end, a sufficient criterion is given in this paper for the one-variable fragment of a semantically defined first-order logic—spanning families of intermediate, substructural, many-valued, and modal logics—to admit a certain natural axiomatization. More precisely, an axiomatization is obtained for the one-variable fragment of any first-order logic based on a variety of algebraic structures with a lattice reduct that has the superamalgamation property, using a generalized version of a functional representation theorem for monadic Heyting algebras due to Bezhanishvili and Harding. An alternative proof-theoretic strategy for obtaining such axiomatization results is also developed for first-order substructural logics that have a cut-free sequent calculus and admit a certain interpolation property.

Quantifying events or entities?—A corpus-based study of universal quantifiers in early child English and child-directed speech

The acquisition of quantifiers is a central topic in cognitive science. The present study investigated the emergence, frequency, and non-target-like production of the universal quantifiers all, every, and each in child English from a linguistic perspective, based on the data from longitudinal naturalistic observation of 10 English-speaking children and their caregivers. We found that the use of these quantifiers as adverbs or in adverbials generally appeared earlier, and was more frequent, than their use as (pre)determiners in early child English. We also found that input frequency exerts a great influence on some aspects of the acquisition of universal quantifiers, for example, the frequency of the predeterminer all, but there are still some patterns that cannot be explained by mere input frequency, such as children’s initial preference for using universal quantifiers in A(dverbial)-quantification and their non-target forms. Their initial overreliance on A-quantification may be explained by event quantification being cognitively less demanding than entity quantification, and their non-target productions likely result from their developing grammatical systems. We argue that the acquisition of universal quantifiers involves multiple factors, such as cognitive complexity, children’s developing grammatical systems, and input frequency, interacting with each other.

Telescoping in incremental quantification

Bumford (2015) argues that universal quantification in dynamic semantics should be analyzed as generalized dynamic conjunction for empirical benefits. However, this analysis is incompatible with the existing telescoping analyses, which use a pluralized dynamic system (van den Berg 1996; Nouwen 2003; Brasoveanu 2007: a.o.). This study aims to resolve this conflict. It is proposed that quantification over events and their participants allows us to account for telescoping without the pluralized dynamic system.

Kinds, properties and atelicity

Since at least Vendler 1967, one of the most widely discussed data points, often viewed as the ultimate test for (a)telicity, is the behavior of durative modifiers with respect to different VP types as in John killed mosquitos/*a mosquito for an hour. In the present paper, I explore a new blend of the two most widespread approaches to this issue, namely (i) the view of durative modifiers as universal quantifiers (e.g., Dowty 1979, a.o.) and (ii) their view as aspect sensitive measure adverbials (e.g., Krifka 1998, a.o.). The blend explored here is based on an economy constraint specific to the scope of adverbial quantification (‘do not weaken’ cf. Bassa Vanrell 2017) combined with the identification of the special role that kinds and properties may play as direct bearers of thematic relations in an event-based semantics.

Four Dialectal Uses of the Adverb Siempre and Their Grammatical Properties

This article analyzes four interpretations of the adverb siempre ‘always’ that do not belong to general Spanish. The continuative and the progressive-comparative interpretations are argued to be calques of Italian, often attested in Rioplatense Spanish. In the first one, siempre is equivalent to Eng. still or ‘continue to + infinitive’, while in the second one it admits paraphrases with more and more, less and less, and the adverbs gradually and progressively. The third interpretation, in which siempre is roughly equivalent to after all, finally, and ‘end up + gerund’, will be argued to be concessive-adversative. This reading is more frequent in Mexico and Central America, but it is also attested in other American countries. The fourth reading is the attenuated interpretation, registered in part of the Andean area. In this meaning, siempre is equivalent to roughly or so so. It is argued that, with the possible exception of the last reading (whose origin is insecure), these different meanings of siempre coincide in the interpretation of this adverb as a universal quantifier, while they differ in the semantic nature of the quantified variable.

Logical extensions of the parametric closure operator

Abstract In the present survey, we consider all logical extensions of the parametric closure operator. Such extensions are obtained by augmenting the parametric closure language with arbitrary logical connectives or the universal quantifier. This gives, in addition to the parametric closure operator, the operators of positive and implicative closure, and also the closure operator with complete system of logical connectives, and the conjunctive-quantifier closure operator. We present basic facts on classifications of the sets Pk generated by these operators.