On Translating a Universal Quantifier and an Existential Quantifier in Terms of Existential Fallacy

2020 ◽  
Vol 25 (2) ◽  
pp. 117-133
Author(s):  
Heungseob Yoon
Keyword(s):  
Universal Quantifier ◽  
Existential Quantifier

Arithmetic definability by formulas with two quantifiers

1992 ◽  
Vol 57 (1) ◽  
pp. 1-11
Author(s):  
Shih Ping Tung
Keyword(s):  
Algebraic Number ◽  
Necessary Conditions ◽  
Algebraic Integer ◽  
Number Fields ◽  
Universal Quantifier ◽  
Existential Quantifier ◽  
Algebraic Number Fields ◽  
Integer Rings

AbstractWe give necessary conditions for a set to be definable by a formula with a universal quantifier and an existential quantifier over algebraic integer rings or algebraic number fields. From these necessary conditions we obtain some undefinability results. For example, N is not definable by such a formula over Z. This extends a previous result of R. M. Robinson.

Extension particles, etc.

1992 ◽  
Vol 4 (2) ◽  
pp. 179-203 ◽  
Author(s):  
Sylvie Dubois
Keyword(s):  
Social Class ◽  
Sociodemographic Factors ◽  
Syntactic Complexity ◽  
Universal Quantifier ◽  
Existential Quantifier ◽  
Discourse Functions ◽  
Age Grading ◽  
Occurrence Patterns ◽  
Good Number

ABSTRACTThe study of the 2700 occurrences of phrase-terminal extension particles (e.g., tout ça ‘all that’, des affaires de même ‘things like that’) in two large corpora of Montréal French reveals that they are typically formed of some combination of a quantifier, a generic and a comparative, and that the particle is optionally prefaced by a connector (the conjunctions puis, et ‘and’, ou ‘or’). The 76 particle types (not counting minor variations) also include a good number of fixed forms (e.g., et cetera) often having an onomatopoeic aspect (e.g., patati patata). Extension particles can be characterized through prosodic, syntactic, and semantic criteria. The analysis bears on the sociodemographic conditioning of overall rates of particle use; of choices within the quantifier, generic, and comparative categories; and of preference for each of four major classes of particle: those containing a universal quantifier, those containing an existential quantifier, those consisting of just a generic and a comparative, and fixed forms. The discourse insertion of the four classes is also analyzed in terms of connector, type of discourse transition, the complexity of the term(s) semantically “extended” by the particle, and the discourse genre. The clearest result pertaining to overall rates of use is an age-grading effect, whereby speakers use fewer particles as they grow older. Within the components, women use more quantifiers than men, and both generics and comparatives are sharply stratified by social class and age. The reconstituted particles tend to favor certain co-occurrence patterns and avoid others more than could be predicted from the component distributions, consistent with a stylistic concord effect. As for the four classes of particle, it is the presence and nature of the connector that have the strongest effects, where puis contrasts with both ou and the null connector, while the complexity of the extended term distinguishes among the classes both by virtue of the number of terms and their syntactic complexity. As is predictable from functional considerations the sociodemographic factors do not contrast the two semantically most distinct classes, involving universal versus existential quantifiers. The linguistic validity of the four classes is confirmed by the fact that their quantitative conditioning is not predictable from the strong sociodemographic conditioning of their component elements, but rather reflects their differential suitability for various discourse functions.

Disjunction in Kannada and Korean

2006 ◽  
Vol 13 ◽  
pp. 197-218
Author(s):  
Youngjun Jang
Keyword(s):  
Word Order ◽  
Universal Quantifier ◽  
Existential Quantifier ◽  
Question Formation ◽  
Syntactic Properties

Abstract. This paper compares disjunction in Kannada and Korean and examines the morpho-syntactic properties of it in these languages, focusing on Kannada -oo/illa and Korean -na. Kannada and Korean are genealogically unrelated, but share SOV word order. It is thus expected that the disjunction head follow its complement. Indeed, Kannada -oo and Korean -na follow their comple-ments. What is truly intriguing is that it shows surprisingly parallel properties. For example, Kan-nada -oo and Korean -na not only yield disjunction but also invoke indirect question interpretation. That is, both of them are used as a disjunctive conjunct as well as a question marker. In this paper, we examine the parallels and differences between the disjunction in these languages and show that the conjunctive and disjunctive reading is expressed in different modes. Under the present analysis, we can readily explain the indirect question formation, wh-scope marking, and the dummy wh-phrases in the oo-complementation. We also show that the existential quantifier interpretation of wh-indefinites plus -oo can be accounted for, assuming -oo to be a wh-question marker. Unlike what Amritavalli (2003) predicts, wh-indefinites plus disjunctive morpheme yields universal quantifier interpretations in languages like English, Japanese, and Korean.

scholarly journals Kwantyfikacyjne i egzystencjalne wykładniki afirmacji na przykładzie języka serbskiego

2015 ◽  
Vol 10 ◽  
pp. 103-119
Author(s):  
Marcin Grygiel
Keyword(s):  
Conceptual Metaphor ◽  
Universal Quantifier ◽  
Existential Quantifier ◽  
Slavic Languages ◽  
Metaphorical Extension ◽  
Logical Rules

Quantifiers and existentials as markers of affirmation in SerbianIn the paper I argue that quantifiers understood as numerical language expressions and the verb ‘to be’ are used to express and intensify affirmation in Serbian and other Slavic languages. I focus on two types of quantifiers: the universal quantifier, represented in Serbian by the lexeme svi and its derivatives, and the existential quantifier associated with the numeral jedan and the verb ‘to be’. Both types of quantifiers in analyzed contexts acquire secondary functions of affirmation markers. However, the scope of this type of affirmation marking is quite limited as very often the same words may be used in negative contexts. As a consequence, it is impossible to describe this function referring to any strict logical rules, but it is better to regard it as a metaphorical extension. Thus, the use of universal quantifier as a marker or intensifier of affirmation is believed to be best described as being based on the conceptual metaphor AFFIRMATION IS COMPLETENESS and the intensification of affirmation in the case of existential quantifier and the verb ‘to be’ relies on the metaphor AFFIRMATION IS EXISTENCE.

scholarly journals Properties of power series of analytic in a bidisc functions of bounded $\mathbf{L}$-index in joint variables

2017 ◽  
Vol 9 (1) ◽  
pp. 6-12 ◽  
Author(s):  
A.I. Bandura ◽  
N.V. Petrechko
Keyword(s):  
Continuous Function ◽  
Power Series ◽  
Series Expansion ◽  
Analytic Functions ◽  
Homogeneous Polynomial ◽  
Necessary Conditions ◽  
Power Series Expansion ◽  
Sufficient Conditions ◽  
Universal Quantifier ◽  
Existential Quantifier

We generalized some criteria of boundedness of $\mathbf{L}$-index in joint variables for analytic in a bidisc functions, where $\mathbf{L}(z)=(l_1(z_1,z_2),$ $l_{2}(z_1,z_2)),$ $l_j:\mathbb{D}^2\to \mathbb{R}_+$ is a continuous function, $j\in\{1,2\},$ $\mathbb{D}^2$ is a bidisc $\{(z_1,z_2)\in\mathbb{C}^2: |z_1|<1,|z_2|<1\}.$ The propositions describe a behaviour of power series expansion on a skeleton of a bidisc. We estimated power series expansion by a dominating homogeneous polynomial with the degree that does not exceed some number depending only from radii of bidisc. Replacing universal quantifier by existential quantifier for radii of bidisc, we also proved sufficient conditions of boundedness of $\mathbf{L}$-index in joint variables for analytic functions which are weaker than necessary conditions.

On the Interval Generalized Coupled Matrix Equations

2018 ◽  
Vol 34 ◽  
pp. 695-717 ◽  
Author(s):  
Marzieh Dehghani-Madiseh
Keyword(s):  
Numerical Technique ◽  
Sufficient Conditions ◽  
Algebraic Approach ◽  
Real Interval ◽  
Matrix Equations ◽  
Universal Quantifier ◽  
Existential Quantifier ◽  
Solution Sets ◽  
Interval Matrices

In this work, the interval generalized coupled matrix equations \begin{equation*} \sum_{j=1}^{p}{{\bf{A}}_{ij}X_{j}}+\sum_{k=1}^{q}{Y_{k}{\bf{B}}_{ik}}={\bf{C}}_{i}, \qquad i=1,\ldots,p+q, \end{equation*} are studied in which ${\bf{A}}_{ij}$, ${\bf{B}}_{ik}$ and ${\bf{C}}_{i}$ are known real interval matrices, while $X_{j}$ and $Y_{k}$ are the unknown matrices for $j=1,\ldots,p$, $k=1,\ldots,q$ and $i=1,\ldots,p+q$. This paper discusses the so-called AE-solution sets for this system. In these types of solution sets, the elements of the involved interval matrices are quantified and all occurrences of the universal quantifier $\forall$ (if any) precede the occurrences of the existential quantifier $\exists$. The AE-solution sets are characterized and some sufficient conditions under which these types of solution sets are bounded are given. Also some approaches are proposed which include a numerical technique and an algebraic approach for enclosing some types of the AE-solution sets.

Effect of Introducing the Universal Quantifier ‘All’ into the Class Inclusion Question

1987 ◽  
Vol 60 (3_part_2) ◽  
pp. 1255-1258
Author(s):  
Ron Gold
Keyword(s):  
Universal Quantifier ◽  
Class Inclusion ◽  
Standard Version ◽  
The Third

The effect of introducing the universal quantifier ‘all’ into the class inclusion question was investigated using 104 children aged 59 to 90 mo. One group of children was asked the standard version of the question, another an ‘all-subset’ version in which ‘all’ preceded the subclass, the third an ‘all-superset’ version with ‘all’ before the superordinate class, and the fourth a ‘double-all’ version with ‘all’ in both locations. When the superordinate class was mentioned last in the question, performance was better on the all-superset and double-all versions than on the standard version. When the subclass was mentioned last, performance was better on the all-superset version only. Performance on the all-subset version did not differ from that on the standard version. The results were explained in terms of the attention-directing role of ‘all’, together with the proposal that performance improves if attention is drawn towards the superordinate class and/or away from the contrast between the subclasses.

scholarly journals The trouble with the second quantifier

4OR ◽  
2021 ◽  
Author(s):  
Gerhard J. Woeginger
Keyword(s):  
Computational Complexity ◽  
Robust Optimization ◽  
Complexity Theory ◽  
Operational Research ◽  
Optimization Problems ◽  
Bilevel Optimization ◽  
Theoretical Background ◽  
Research Community ◽  
Universal Quantifier ◽  
Computational Complexity Theory

AbstractWe survey optimization problems that allow natural simple formulations with one existential and one universal quantifier. We summarize the theoretical background from computational complexity theory, and we present a multitude of illustrating examples. We discuss the connections to robust optimization and to bilevel optimization, and we explain the reasons why the operational research community should be interested in the theoretical aspects of this area.

scholarly journals Relaxing the universal quantifier of the division in fuzzy relational databases

2001 ◽  
Vol 16 (6) ◽  
pp. 713-742 ◽  
Author(s):  
José Galindo ◽  
Juan M. Medina ◽  
Juan C. Cubero ◽  
M. Teresa García
Keyword(s):  
Relational Databases ◽  
Universal Quantifier

scholarly journals Intonational effects on English scopally-ambiguous sentences

2020 ◽  
Vol 73 (3) ◽  
pp. 13-36
Author(s):  
Mien-Jen Wu ◽  
Tania Ionin
Keyword(s):  
Native English Speakers ◽  
Judgment Task ◽  
Subject Position ◽  
English Speakers ◽  
Universal Quantifier ◽  
Sentential Negation ◽  
Prior Literature ◽  
The Relationship ◽  
Acceptability Judgment

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.

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