Quantifier Scope Research Articles

Lexicon and Logic: A Corpus-Based Investigation Into a Connection Between Prepositional Senses and Quantifier Scope

Abstract Previous research has indicated that abstract grammatical rules and forms fall short of predicting quantifier scope and that lexical/pragmatic knowledge plays a significant part in quantifier scope disambiguation (QSD). More recent works have argued that world knowledge in the form of relations among objects may be salient to QSD. This paper contributes to this line of research by providing support to the claim that there is a connection between our lexical knowledge about preposition meanings and quantifier scope. More specifically, we propose that certain prepositional senses encode dependency relations that have an effect on scope-taking preferences. For example, the preposition of expressing ‘part-whole sense’ contributes to our choice of the inverse scope reading for the construction a day of every month by introducing a dependency between wholes (months) and their respective parts (days). Quantifying over this dependency yields the inverse scope reading: for every month, there is a different day that belongs to it (every month > a day). Furthermore, universal quantification in locative and temporal prepositional phrases tends to support inverse scope. For example, the locative preposition on — as in a store on each side of the street — implies ‘disjointness’ (objects do not occupy more than one place at a time), and hence can be interpreted as a dependency between each side of the street and the respective stores located on them. Quantifying over this dependency yields the inverse scope reading: for each side of the street, there is a different store located on it (each side of the street > a store). For studying the connection between prepositional senses and quantifier scope in the wild, we use a scope-disambiguated corpus created by AnderBois et al. ( 2012), additionally annotated with prepositional senses using the Semantic Network of Adposition and Case Supersenses (SNACS) scheme proposed in Schneider et al. ( 2018, 2020). The results of the corpus study combined with psycholinguistic experiments support the claim made here that certain prepositional senses are strong predictors of quantifier scope.

How abstract are logical representations? The role of verb semantics in representing quantifier scope

Language comprehension involves the derivation of the meaning of sentences by combining the meanings of their parts. In some cases, this can lead to ambiguity. A sentence like Every hiker climbed a hill allows two logical representations: One that specifies that every hiker climbed a different hill and one that specifies that every hiker climbed the same hill. The interpretations of such sentences can be primed: Exposure to a particular reading increases the likelihood that the same reading will be assigned to a subsequent similar sentence. Feiman and Snedeker (2016) observed that such priming is not modulated by overlap of the verb between prime and target. This indicates that mental logical representations specify the compositional structure of the sentence meaning without conceptual meaning content. We conducted a close replication of Feiman and Snedeker’s experiment in Dutch and found no verb-independent priming. Moreover, a comparison with a previous, within-verb priming experiment showed an interaction, suggesting stronger verb-specific than abstract priming. A power analysis revealed that both Feiman and Snedeker’s experiment and our Experiment 1 were underpowered. Therefore, we replicated our Experiment 1, using the sample size guidelines provided by our power analysis. This experiment again showed that priming was stronger if a prime-target pair contained the same verb. Together, our experiments show that logical representation priming is enhanced if the prime and target sentence contain the same verb. This suggests that logical representations specify compositional structure and meaning features in an integrated manner.

An experimental investigation into scope rigidity in written Mandarin.

Mandarin Chinese is claimed to be a scope-rigid language, as its doubly-quantified simple transitive sentences are unambiguous with surface scope only and no inverse scope available. However, it has been debated whether Mandarin Chinese allows inverse scope in some syntactic environments other than simple transitives. This paper investigates whether scope rigidity as a property of the grammar of Mandarin prevents scope ambiguity in different syntactic environments and what factors influence scope interpretations. Using a Truth-Value Judgment task, we tested the judgments of 98 Mandarin Chinese native speakers on transitive sentences containing both a subject and object quantifier under adverbial clauses. The results show that inverse scope reading is considered available for doubly-quantified transitives under adverbial clauses, although there are intra-participant variances. The results challenge the well-established approaches to quantifier scope in Mandarin and call for rethinking the long-standing dichotomy view of quantifier scope in languages. We also found bimodal distribution on the acceptance of inverse scope readings, suggesting that there may be two different populations of native speakers with two different grammars. In addition, we also observed other factors that may affect scope behaviors, including clause type, presence of aspect marker, verb type, and numbers.

Presupposition Projection from the Scope of Quantifiers in Mandarin Chinese

Quantifiers, words that indicate the quantity of the object, have been proven to alter the presupposition readings in a statement. This paper aims at examining the effect of quantifiers on the presupposition readings, namely universal, existential, and nonpresuppositional readings, in Chinese settings by surveying native Chinese speakers. This paper finds out that all usually has a universal reading and some usually has a existential reading, while all and none of have simialr percentage of non-pressuppositional readings.

Corpus evidence for the role of world knowledge in ambiguity reduction: Using high positive expectations to inform quantifier scope

Every-negation utterances (e.g., Every vote doesn’t count) are ambiguous between a surface scope interpretation (e.g., No vote counts) and an inverse scope interpretation (e.g., Not all votes count). Investigations into the interpretation of these utterances have found variation: child and adult interpretations diverge (e.g., Musolino 1999) and adult interpretations of specific constructions show considerable disagreement (Carden 1973, Heringer 1970, Attali et al. 2021). Can we concretely identify factors to explain some of this variation and predict tendencies in individual interpretations? Here we show that a type of expectation about the world (which we call a high positive expectation), which can surface in the linguistic contexts of every-negation utterances, predicts experimental preferences for the inverse scope interpretation of different every-negation utterances. These findings suggest that (1) world knowledge, as set up in a linguistic context, helps to effectively reduce the ambiguity of potentiallyambiguous utterances for listeners, and (2) given that high positive expectations are a kind of affirmative context, negation use is felicitous in affirmative contexts (e.g., Wason 1961).

Ranges: composite measure phrases, modified numerals, and choice functions

Range expressions such as between 3 and 8, from 3 to 8, and 3 through 8 resemble modified numerals such as at least 3 and have sometimes been mentioned under that rubric. This paper shows that they are crucially different in their distribution, the readings available to them, and their behavior with respect to quantifiers, and more generally that they have an intricate grammar of their own. We distinguish three classes of readings they can receive: singleton punctual readings, on which they often give rise to ignorance inferences; set punctual readings, which arise chiefly in the scope of quantifiers; and interval readings, where the range is interpreted exhaustively. We propose an analysis on which range expressions denote choice functions over degrees, which can in the right circumstances be parameterized.

Event plurality & quantifier scope across clause boundaries

Legend has it that quantifiers cannot scope out of finite clauses. But whileislands for quantifier raising might exist, finite clauses are not that: We identifya novel environment which productively facilitates scoping universal quantifiersout of embedded clauses, involving the manipulation of event structure. With thehelp of the perfect on an embedding verb and certain adverbials that presuppose abuildup towards a result state (by noon, eventually, at long last), embedded universalquantifiers can more readily take extrawide scope. We describe, account for, anddiscuss restrictions to this effect, and conclude that scoping quantifiers out of finiteclauses is not banned by syntactic constraints, although context or processing mightfavor narrow scope readings.

Semantic scope in Q-float constructions: An experimental investigation

Researchers have long assumed that the semantic scope of floating quantifiers is frozen with respect to scope-taking elements. This fact, among others, has been used to motivate an adverbial analysis of floating quantifiers and to argue against stranding/movement analyses. More recent work has cast doubt on this assumption, showing that in many languages, floating quantifiers and numerals can exhibit inverse scope. This paper contributes to this debate by experimentally investigating semantic scope of floating quantifiers with respect to negation in (American) English. The results of a picture truth-value task reveal that Q-float does not affect quantifier scope with respect to negation; just like non-floating quantifiers, floating quantifiers exhibit inverse scope as well as surface scope. This result is significant in not only providing support for movement analyses, but also in showing that the distribution of floating quantifiers can be a reliable diagnostic of the positions of lower copies in a movement dependency.

Chinese quantifier scope, concord, and Lexical Resource Semantics

This paper considers Chinese quantifier scope, an important, outstanding area of Chinese linguistics. In particular, there are two open questions on the subject: (1) the guiding principles that determine (a) the scopal readings of quantifiers and (b) the sometimes mandatory co-occurrence of the universal quantifier mei (every) and the universal adverb dou, and (2) the semantic functions of mei and dou and their connection to the co-occurrence of these words. We reappraise three prior accounts of these subjects, reason through their consequences on some exemplary data, offer a new explanation based upon concord, a mechanism that is commonplace in many languages, and formulate it in lexical resource semantics (LRS). We use two principles adapted from Richter and Sailer's (2004) analysis of negative concord, expanded with a new quantifier order constraint to generate a coherent answer to the two aforementioned questions.

C-command constraints in German: A corpus-based investigation

AbstractReinhart (1983) proposed that quantificational binding is subject to a surface c-command condition. Her claim has been widely accepted in the literature on the syntax-semantics interface. However, Barker (2012) presented systematic counterevidence against the c-command requirement from English. The current paper addresses the role of c-command constraints in the grammar of three phenomena in German: relative quantifier scope, quantificational binding, and negative polarity. The results of a large corpus study are presented that demonstrate empirically that scope of one quantifier over another, quantificational binding, and the licensing of negative polarity items in German are systematically possible in structural configurations where surface c-command cannot reasonably be assumed to obtain. Further corpus evidence is produced which shows that the non-c-commanding quantifiers in the examples typically occur in contexts where the set they quantify over is discourse-old or easy to accommodate. The overall picture that emerges from the empirical evidence is that topicality motivates wide scope, and scope rather than c-command licenses negative polarity items and bound pronouns.

Accessing the availability of inverse scope in German in the covered box paradigm

This paper presents the results of a novel experimental approach to relative quantifier scope in German that elicits data in an indirect manner. Applying the covered-box method (Huang et al. 2013) to scope phenomena, we show that inverse scope is available to some extent in the free constituent order language German, thereby validating earlier findings on other syntactic configurations in German (Radó & Bott 2018) and empirical claims on other free constituent order languages (Japanese, Russian, Hindi), as well as recent corpus findings in Webelhuth (2020). Moreover, the results of the indirect covered-box experiment replicate findings from an earlier direct-query experiment with comparable target items, in which participants were asked directly about the availability of surface scope and inverse scope readings. The configuration of interest consisted of canonical transitive clauses with deaccented existential subject and universal object QPs, in which the restriction of the universal QP was controlled for by the context.

Relative measurement and scope in Mandarin

It is well known that the scope of quantifiers is not uniform: different quantifiers exhibit different scope properties. This paper examines the scope of a relatively understudied quantificational DP—relative measure phrases that contain proportional number expressions like 40%, one third, half, etc and relate one quantity to another. Based on relative measurement constructions in Mandarin, I observe that a relative measure phrase exhibits distinct scope patterns when it participates in the so-called ‘conservative’ and ‘non-conservative’ reading (terminology from Ahn & Sauerland (2017)). I pursue a decompositional analysis to account for the scopal difference: a relative measure phrase is decomposed into a degree quantifier denoted by the proportional number expression and a counting quantifier. A proportional number expression can take DP-internal scope or DP-external scope. Different scope taking strategies face different constraints, which in turn give rise to distinct scope possibilities.

Native and second language processing of quantifier scope ambiguity

The present study investigates native (L1) and second language (L2) processing of scope ambiguities in English sentences containing the universal quantifier every in subject NP and negation. Previous studies in L1 and L2 processing of scope ambiguities have found speakers to generally employ a ‘minimal effort’ principle that highly prefers the surface scope reading regardless of contextual support because accessing the inverse scope reading incurs significant processing cost. The present study compared L1 and L2 scope judgments and processing strategies of sentences such as Every horse didn’t jump over the fence and examined whether the two groups differ in their speed and manner of analysis. Thirty native English speakers and 42 Korean learners of English participated in a self-paced reading/interpretation task that has context (ambiguous vs. unambiguous) and scope reading (surface vs. inverse) as variables. The results revealed significant differences in scope endorsement rates with L2 learners arriving at the surface scope as the dominant reading and L1 learners’ judgments being highly dependent on contextual ambiguity. Moreover, L1 vs. L2 differences in processing strategies were found: L2 learners exhibited a strong tendency to arrive at the most economical interpretation while L1 speakers consulted detailed syntactic and semantic rules of computation.

Scope freezing and object shift in Ukrainian: Does Superiority matter?

AbstractThis remark presents novel evidence on Ukrainian specificity‐inducing object shift in its interaction with quantifier scope, evidence suggesting a generalization that whatever scope interpretations are established in the postverbal field will carry over into the preverbal field. We point out that the data present a serious challenge to the Superiority account of scope freezing, since that account predicts that object shift of a QP will always freeze scope with respect to another object QP, contrary to fact. Furthermore, while Ukrainian object shift does not obey Holmberg’s Generalization, we argue that it is nevertheless fully comparable to Scandinavian object shift. We propose to account for the data with a modified version ofcyclic linearization. Cyclic linearization accounts for the crosslinguistic differences with respect to object shift and also derives the peculiar object shift–QP scope interaction patterns we observe, which remain obscure on the Superiority account of scope freezing.

Glue Semantics

Glue Semantics (Glue) is a general framework for semantic composition and the syntax–semantics interface. The framework grew out of an interdisciplinary collaboration at the intersection of formal linguistics, formal logic, and computer science. Glue assumes a separate level of syntax; this can be any syntactic framework in which syntactic structures have heads. Glue uses a fragment of linear logic for semantic composition. General linear logic terms in Glue meaning constructors are instantiated relative to a syntactic parse. The separation of the logic of composition from structural syntax distinguishes Glue from other theories of semantic composition and the syntax–semantics interface. It allows Glue to capture semantic ambiguity, such as quantifier scope ambiguity, without necessarily positing an ambiguity in the syntactic structure. Glue is introduced here in relation to four of its key properties, which are used as organizing themes: resource-sensitive composition, flexible composition, autonomy of syntax, and syntax/semantics non-isomorphism.

When pragmatics matters more for truth-value judgments: An investigation of quantifier scope ambiguity

Investigations of linguistic meaning rely crucially on truth-value judgments, which assess whether a sentence can truthfully describe a given scenario. In investigations of language acquisition, truth-value judgments are used to assess both the target knowledge adults have and the developing knowledge children have at different ages. On the basis of truth-value judgments, researchers have concluded that differences between how children resolve ambiguous utterances and how adults do so persist until at least age five. Current explanations compatible with the experimental data attribute these differences to both grammatical processing and pragmatic factors. Here, we use computational cognitive modeling to formally articulate one hypothesis about the ambiguity-resolution process that underlies child and adult judgments in a truth-value judgment task; crucially, the model can separate out the individual contributions of specific grammatical processing and pragmatic factors to the resulting judgment behavior. We find that pragmatic factors play a larger role than grammatical processing factors in explaining children’s non-adult-like ambiguity resolution behavior. Interestingly, the model predicts qualitative similarity between child and adult ambiguity resolution. Given this prediction, we then extend our model to show how the same processes may be active in adult ambiguity resolution. This result supports continuity in the development of ambiguity resolution, where children do not qualitatively change how they resolve ambiguity in order to become adult-like. We discuss the implications of our results for acquisition more generally, including both theories of development and methods for assessing that development, as well as the generalizability of this model of ambiguity resolution beyond the specific cases we consider.

Generalised Crossover

Crossover (CO) is a constraint on anaphoric dependencies, according to which, quantifier scope can feed pronominal anaphora unless the anaphoric expression precedes the quantifier. We demonstrate that effects reminiscent of CO arise with presupposition as well, and propose to generalise CO as follows: Projective content (quantifier scope, presupposition projection, etc.) feeds semantic dependencies (pronominal anaphora, presupposition satisfaction), unless the semantically dependent expression precedes the trigger of the projective content. We call this generalisation, Generalised Crossover (GCO). Although we cannot offer a full explanation for GCO in this paper, we will discuss its implications for recent theories of CO.

Does explicit instruction affect L2 linguistic competence? An examination with L2 acquisition of English inverse scope

This article investigates whether explicit instruction can affect second language (L2) competence in the domain of English quantifier scope. An intervention study was conducted with L1-Mandarin L2-English learners in order to examine (1) whether these learners can learn inverse scope for the structure on which they are instructed (double-quantifier configuration: A dog scared every man; quantifier-negation configuration: Every sheep did not jump over the fence); (2) whether they can correctly generalize availability of inverse scope from the configuration on which they are instructed to one on which they are not instructed; and (3) whether learners overgeneralize inverse scope to a superficially similar configuration that does not allow inverse scope. Following Schwartz (1993), generalization is taken to be a hallmark of true acquisition (= changes to linguistic competence) as opposed to learning. The results show that learners successfully learn inverse scope for the configuration on which they are instructed, but do not generalize availability of inverse scope to the other configuration. Moreover, learners instructed on double-quantifier configurations overgeneralize availability of inverse scope to island configurations such as There is one dog which scared every man. The findings indicate that in this domain, explicit instruction does not affect linguistic competence.

Ditransitive Asymmetries and Quantifier Scope in Korean

Ditransitive Asymmetries and Quantifier Scope in Korean

Quantifier scope and information structure in Greek

In this paper, we investigate the availability of inverse scope interpretation in doubly-quantified sentences in Greek. A rather coarse and, as we show, inaccurate empirical generalization is that languages with relatively free word order do not have inverse scope readings, since movement is always spelled-out. In Greek there is little experimental work testing inverse scope with DP-quantifiers and there is considerable disagreement among linguists regarding its availability. Our goal is two-fold: i) to contribute towards a better understanding of the empirical facts and ii) to explore the relation between inverse scope availability and the syntax and semantics of different configurations. As we show, inverse scope is generally acceptable by Greek speakers, with the exception of environments with Clitic Left Dislocation. Our data add up to recent studies in other languages which suggest that the critical factor for the (non)-availability of inverse scope is the properties of each individual construction and not a dichotomy between different types of languages.