Existential Quantification Research Articles

A contextualist treatment of negative existentials

Abstract In this paper, I want to vindicate the contextualist treatment that is typically applied by artefactualists on fictional entities (ficta) both to general and to singular negative existentials. According to this treatment, the truth value of a negative existential, whether general or singular, changes according to whether the existential quantifier or the first-order existence predicate is contextually used as respectively ranging over and applying to a restricted or an unrestricted domain of beings. In (2003), Walton has criticized this treatment with respect to singular negative existentials in particular. First of all, however, as (Predelli, Stefano. 2002. ‘Holmes’ and Holmes. A Millian analysis of names from fiction. Dialectica 56. 261–279) has shown, this treatment can be applied to singular predications in general, independently of the existential case. Moreover, not only does applying it to singular negative existentials explain why we may contextually use the quantifier restrictedly in general negative existentials, but also it accounts for why comparative negative existentials, both singular and general, may have different truth values as well depending on the comparison group they mobilize.

A New Multi-stage Secret Sharing Scheme for Hierarchical Access Structure with Existential Quantifier

Multi-stage secret sharing scheme is practical in the case that there is a security system with m ordered checkpoints.It is natural to divide the m checkpoints into m different levels. There are m different secrets, and eachof them with a different importance corresponds to a checkpoint/level. The participants are also divided intom disjoint levels as they do in the hierarchical threshold access structure. Hierarchical threshold access structurewith the existential quantifier ( HTAS∃ ) does not cover the common practice that at least a few numbersof high-ranking participants are required to be involved in any recovery of the secret. The popular schemeswith hierarchical access structure were needed to check many matrices for non-singularity. We propose amulti-stage secret sharing scheme for HTAS∃ , and the tools are based on the linear homogeneous recurrencerelations (LHRRs) and one-way functions. We give the HTAS∃ a modification, so that this hierarchical accessstructure can satisfy the common practice. In our scheme, if the participants are divided into m levels, thereusually has m secrets. But before the (j − 1)-th secret is recovered, the j-th secret cannot be recovered. Ourscheme is a computational secure. The proposed scheme requires a share for each participant and the shareis as long as each secret. Our scheme has high efficiency by comparing with the state-of-the-art hierarchicalsecret sharing schemes.

Attempts

It’s generally assumed that, if an agent x acts by ϕ-ing, then there occurs an event which is x’s ϕ-ing. But what about when an agent tries to do something? Are there such things as attempts? The standard answer is ‘Yes’. But in a series of articles, and now a book, David-Hillel Ruben has argued that the answer is ‘No’: what happens when x tries to ϕ isn’t that an attempt occurs; rather, what happens is simply that a certain subjunctive conditional fact obtains; x tries to ϕ just in case, had all the necessary conditions for success obtained, x would have intentionally ϕ-ed. I defend the existence of attempts. Following Ruben, I frame the issue in terms of the logical form of trying sentences (i.e. sentences which report that an agent tried to do such-and-such). Against Ruben’s view that such sentences express subjunctive conditionals, I argue that they express existential quantifications over attempts qua events. Thus, trying sentences are true only if attempts qua events exist.

On indefinite subjects in Mandarin

Abstract This study investigates the licensing conditions and interpretational variability of indefinite subjects in Mandarin. Against the ‘definiteness’ constraint of subject in Mandarin (Chao 1968; Li and Thompson 1981), three types of indefinite subjects are identified in the subject position, but they exhibit different scope behaviors: (i) you-nominals are ambiguous between a wide scope and a narrow scope, and (ii) thetic subjects are narrow-scope taking, and (iii) ‘cardinal’ subjects are scopeless. Following Cohen and Erteschik-Shir (2002), we propose that the former two types of indefinite subjects are focus elements and they fall into the position of nuclear scope, where they receive an existential interpretation, and cardinal subjects are topics and they serve as restrictor to some generic operator. Moreover, the wide/narrow scope readings of you-nominals are distinguished from each other in terms of whether a topic domain is available or not, which may serve a domain restrictor to the existential quantifier bound to you-nominals (Portner 2002).

What might but must not be

AbstractWe examine an objection to analysing the epistemic ‘might’ and ‘may’ as existential quantifiers over possibilities. Some claims that a proposition “might” be the case appear felicitous although, according to the quantifier analysis, they are necessarily false, since there are no possibilities in which the proposition is true. We explain such cases pragmatically, relying on the fact that ‘might’-sentences are standardly used to convey that the speaker takes a proposition as a serious option in reasoning. Our account explains why it makes sense to utter these sentences despite their being literally false and why their falsity is easily missed.

Some notes on outro in Portuguese

This paper studies the syntactic behavior of outro(s) in Brazilian and European Portuguese. Starting from the syntax of its Italian counterpart un altro/(degli) altri, we argue that outro(s)in prenominal position is neither an adjective nor a determiner, but an existential quantifier and that the presence of the indefinite article, um outro/uns outros, gives rise to a complex existential quantifier, like the corresponding Italian form. We also argue that outro(s) and um outro/uns outros do not specialize for different interpretations since they both substantially show the same ambiguity (one/some more or a/some different one(s)) and behave in the same way in relation to possible semantic interpretations typical of existential quantifiers

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.

Jeszcze trochę hałasu o nic. Pewna logiczna analiza nicości

Nothingness is a perennial subject of philosophical inquiry. From the logical point of view, the problem is that “nothing” is an ambiguous word: it can be used either as a negated existential quantifier or as a singular term. If it is used as a singular term, then it refers to nothing at all. In this paper, a number of recent formal treatments of nothingness are critically discussed. The author proposes some new logical approaches to nothingness, involving notions of generalized quantifiers, Meinongian objects, and aspectual objects.

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.

Flexibility index and design of chemical systems by cylindrical algebraic decomposition

The traditional methods for the solution of flexibility index and design problems are mainly developed by numerical calculation methods. In this work, a new solution approach is proposed for chemical systems described by polynomials to deduce explicit expressions of flexibility index on the value of the continuous design variables without solving any optimization problems. First, the flexibility index and design problems are reformulated as an existential quantifier model. Then, the cylindrical algebraic decomposition (CAD) method is introduced to project the solution space onto the dimension of design variables, flexibility index and uncertain parameters. Last, the analytical expressions between design variables and flexibility index can be deduced by the inscribed hyperrectangle checking rule. The case studies show that the proposed method is applicable to relatively small- or medium- scaled problems and the explicit relationship between the flexibility index and design variables can be deduced, regardless of linear or nonlinear systems.

PUNCTUAL CATEGORICITY AND UNIVERSALITY

AbstractWe describe punctual categoricity in several natural classes, including binary relational structures and mono-unary functional structures. We prove that every punctually categorical structure in a finite unary language is${\text {PA}}(0')$-categorical, and we show that this upper bound is tight. We also construct an example of a punctually categorical structure whose degree of categoricity is$0''$. We also prove that, with a bit of work, the latter result can be pushed beyond$\Delta ^1_1$, thus showing that punctually categorical structures can possess arbitrarily complex automorphism orbits.As a consequence, it follows that binary relational structures and unary structures are not universal with respect to primitive recursive interpretations; equivalently, in these classes every rich enough interpretation technique must necessarily involve unbounded existential quantification or infinite disjunction. In contrast, it is well-known that both classes are universal for Turing computability.

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.

INFINITARY GENERALIZATIONS OF DELIGNE’S COMPLETENESS THEOREM

AbstractGiven a regular cardinal $\kappa $ such that $\kappa ^{<\kappa }=\kappa $ (or any regular $\kappa $ if the Generalized Continuum Hypothesis holds), we study a class of toposes with enough points, the $\kappa $ -separable toposes. These are equivalent to sheaf toposes over a site with $\kappa $ -small limits that has at most $\kappa $ many objects and morphisms, the (basis for the) topology being generated by at most $\kappa $ many covering families, and that satisfy a further exactness property T. We prove that these toposes have enough $\kappa $ -points, that is, points whose inverse image preserve all $\kappa $ -small limits. This generalizes the separable toposes of Makkai and Reyes, that are a particular case when $\kappa =\omega $ , when property T is trivially satisfied. This result is essentially a completeness theorem for a certain infinitary logic that we call $\kappa $ -geometric, where conjunctions of less than $\kappa $ formulas and existential quantification on less than $\kappa $ many variables is allowed. We prove that $\kappa $ -geometric theories have a $\kappa $ -classifying topos having property T, the universal property being that models of the theory in a Grothendieck topos with property T correspond to $\kappa $ -geometric morphisms (geometric morphisms the inverse image of which preserves all $\kappa $ -small limits) into that topos. Moreover, we prove that $\kappa $ -separable toposes occur as the $\kappa $ -classifying toposes of $\kappa $ -geometric theories of at most $\kappa $ many axioms in canonical form, and that every such $\kappa $ -classifying topos is $\kappa $ -separable. Finally, we consider the case when $\kappa $ is weakly compact and study the $\kappa $ -classifying topos of a $\kappa $ -coherent theory (with at most $\kappa $ many axioms), that is, a theory where only disjunction of less than $\kappa $ formulas are allowed, obtaining a version of Deligne’s theorem for $\kappa $ -coherent toposes from which we can derive, among other things, Karp’s completeness theorem for infinitary classical logic.

Where is ‘There is’ in ‘∃’?

ABSTRACT The paper offers a survey of four key moments in which symbolisms for quantification were first introduced: §§11–2 of Frege’s Begriffsschrift (1879); Peirce’s ‘Algebra of Logic’ (1885); Peano’s ‘Studii di Logica matematica’ (1897); and *9 (‘replaced’ by *8 in the second edition) of Whitehead and Russell’s Principia Mathematica (1910). Despite their divergent aims, these authors present substantially equivalent visions of what their differing symbolisms express. In each case, some passage suggests that one (but not the only) way to render one of the symbols into ordinary-language words (German, English and Italian) is to say that there is something or some thing(s) exist(s). Exactly how this comes out varies from language to language, but the point remains the same. As a result, in almost all recent logic manuals that introduce ‘∃’, some passage says that the symbol means ‘there is’ or ‘there exists’, and the tradition has grown up of labelling ‘∃’ ‘the existential quantifier’. Some considerations are offered for deprecating this reading of ‘∃’ and the label adopted for it, and for preferring to read it as ‘for some (at least one)’ and for speaking of the ‘particular quantifier’.

La variación formal de los cuantificadores en catalán: estudio diacrónico (siglos XV‒XX)

AbstractThis article studies the formal variation of the existential quantifiers u/un (‘one; a, an’), algú/algun (‘someone; some’), ningú/ningun (‘no one, anyone; any’) and the distributive universal quantifier cada u/cada un (‘everyone’) in Catalan. The research is based on an extensive diachronic corpus of texts written between the 15th and 20th centuries. The author classifies the syntactic structures of these quantifiers and analyses their meaning and formal vacillations: apocopated form (without ‑n) vs. non-apocopated form (with ‑n). Although hesitations tend to disappear gradually during the period under analysis, the uses of these quantifiers change in Catalan dialects. In fact, distinct geographical areas adopt different distributions of form and function. These linguistic changes are explained, highlighting the mutual influences and interactions between phono-syntactic, phonological, analogical and pragmatic factors.

Enhanced Unsatisfiable Cores for QBF: Weakening Universal to Existential Quantifiers

We introduce an enhanced notion of unsatisfiable cores for QBF in prenex CNF that allows to weaken universal quantifiers to existential quantifiers in addition to the traditional removal of clauses. The resulting unsatisfiable cores can be different from those of the traditional notion in terms of syntax, standard semantics, and proof-based semantics. This not only gives rise to explanations of unsatisfiability but, via duality, also leads to diagnoses and repairs of unsatisfiability that are not obtained with traditional unsatisfiable cores. We use a source-to-source transformation on QBF in PCNF such that the weakening of universal quantifiers to existential quantifiers in the original formula corresponds to the removal of clauses in the transformed formula. This makes any tool or method for the computation of unsatisfiable cores of the traditional notion available for the computation of unsatisfiable cores of our enhanced notion. We implement our approach as an extension to the QBF solver DepQBF, and we perform an extensive experimental evaluation on a subset of QBFLIB. We illustrate with several case studies that helpful information can be provided by unsatisfiable cores of our enhanced notion.

The many functions of Cuzco Quechua =<i>pas</i>: implications for the semantic map of additivity

The additive enclitic =pas of Cuzco Quechua is multifunctional: besides marking additivity it also participates in the marking of concessivity, epistemic possibility and the formation of non-specific indefinite pronouns. This paper provides a description of these functions and proposes that they all involve a presupposition of existential quantification over alternatives. Their differences result from the type of alternatives quantified over, namely focus, epistemic or wh-alternatives. The particular clustering of functions found with =pas has implications for the semantic map of additivity proposed by Forker (2016), and presents a counterexample to three implicational universals it encapsulates. Modifications to the map are proposed to accommodate =pas, including connecting it with the semantic map of modality, and recognizing scalar additivity as a subtype of additivity.

The origin and architecture of existential indeterminates in Okinawan

In a number of languages, an indeterminate is combined with various particles to yield different indefinite pronouns. This has been called an indeterminate system (Kuroda 1965, Cheng 1991, Haspelmath 1997, Jayaseelan 2001). As Haspelmath (1997) and Jayaseelan (2001) observe, existential indeterminates are often built with disjunction markers. On the other hand, a disjunction particle and a question particle are often morphologically identical cross-linguistically (see Hagstrom 1998, Jayaseelan 2001). Thus, a question that I ask here is whether the alleged homophony between a disjunction marker and a marker that forms an existential quantifier is principled (Jayaseelan 2001, Szabolcsi et al. 2014) or coincidental (Haspelmath 1997, Cable 2010). In this paper, I argue that the observation about homophony is misguided and hence support Haspelmath’s hypothesis, based on the data obtained from my fieldwork on Okinawan, an endangered Ryukyuan language. I propose an analysis where existential indeterminates in Okinawan have a clausal structure of an embedded question and are derived by deletion.

Implicaturas generalizadas en español: un abordaje experimental

Las implicaturas conversacionales generalizadas (ICG) son un tipo de inferencia pragmática que se caracteriza por una derivación que sigue ciertas regularidades y que es relativamente independiente del contexto de situación (Grice, 1989). Existen dos modelos de procesamiento sobre este fenómeno desde una perspectiva cognitiva (Noveck & Reboul, 2008): 1) el modelo del procesamiento por default (Levinson, 2000) sostiene que el significado pragmático de las ICG se procesa automáticamente y que el contexto interviene tardíamente; 2) el modelo de procesamiento guiado por el contexto (Sperber & Wilson, 1995) considera que la información contextual interviene tempranamente para iniciar el proceso de derivación. Diversos estudios experimentales han cuestionado las hipótesis de estos modelos (Bezuidenhout & Cutting, 2002; Breheny, Katsos & Williams, 2006), sin embargo, a pesar de utilizar las mismas metodologías arribaron a resultados contrapuestos. En este trabajo reportamos los resultados de un experimento de juicios de aceptabilidad realizado con la implicatura escalar producida por el cuantificador algunos (Horn, 1984). Los resultados sugieren que el contexto que precede a la implicatura influye en su procesamiento tardíamente, en línea con las predicciones del modelo por default.

The asymmetric behavior of English negative quantifiers in negative sentences

In this paper, the unexpected behavior of object negative quantifiers in some diagnostic tests of sentential negation is accounted for within a Minimalist framework assuming that: (i) negative quantifiers decompose into negation and an existential quantifier; (ii) negative quantifiers are multidominant phrase markers, as Parallel Merge allows the verb to c-select their existential part but not their negative part, thus giving negation remerge flexibility; (iii) tag questions involveor-coordination of TPs, andneither/soclauses involveand-coordination of TPs; (iv) two positions for sentential negation are available in English, one below TP (PolP2), and one above TP (PolP1). Activation of either PolP1or PolP2in the absence of other scope-taking operators corresponds to two distinct grammars. If PolP1is active, the negative part of an object negative quantifier remerges in its Specifier valuing the [upol: ] feature of Pol1as negative ([upol:neg]) while skipping the TP-domain. As no negative formal feature is present in the TP, a negative question tag is required, as well asso-coordination,too-licensing andYes, I guess so‘expression of agreement’. Conversely, if PolP2is active, the negative part of the object negative quantifier remerges in the TP-domain (in Spec, PolP2), thus requiring a positive question tag,neither-coordination,either-licensing, andNo, I guess not.