Quantifier Scope Research Articles

Is Adult Second Language Acquisition Defective?

There is a large literature showing that adult L2 learners, in contrast to children, often fail to acquire native-like competence in the second language. Because of such age effects, adult L2 learning is often viewed as “fundamentally different” from child acquisition and defective in some way. However, adult L2 learners do not always do worse than child learners. Several studies (e.g., Sasaki, 1997; Dąbrowska and Street, 2006; Street, 2017; Dąbrowska, 2019) found considerable overlap between L1 and L2 speakers’ performance on tasks tapping morphosyntactic knowledge. Crucially, these studies used grammatical comprehension tasks (e.g., picture selection) to test mastery of “functional” grammar (i.e., grammatical contrasts which correspond to a clear difference in meaning, such as the assignment of agent and patient roles in sentences with noncanonical word order and quantifier scope). In contrast, most ultimate attainment studies (e.g., Johnson and Newport, 1989; Flege et al., 1999; DeKeyser, 2000; DeKeyser et al., 2010) used a grammaticality judgment task (GST) which assessed mastery of “decorative” grammar, i.e., grammatical morphemes such as tense and agreement markers which make relatively little contribution to the meaning conveyed by a sentence. In this study, we directly compared native speakers, late immersion learners, and classroom foreign language learners on tasks assessing both aspects of grammar. As in earlier studies, we found significant differences between native speakers and both non-native groups in performance on “decorative” grammar, particularly when performance was assessed using spoken rather than written stimuli. However, the differences in performance on the “functional” grammar task were much smaller and statistically non-significant. Furthermore, even in the “decorative” grammar task, there was more overlap between native speakers and late L2 learners than reported in earlier research. We argue that this is because earlier studies underestimated the amount of variation found in native speakers.

Children's interpretation of negation and quantifier scope in L3 English

AbstractLanguages differ in the preferences for the interpretation of the scope relation between negation and a quantifier. This study investigates the understudied issue of how interpretive preferences associated with a quantifier scope in learners’ L1 and L2 affect their scope interpretations in L3 acquisition. Based on the current models of L3 acquisition, we tested which language, L1 or L2, exerts a stronger effect on the L3 acquisition of quantifier scope. To this end, the study involved two groups of multilingual children (11–13 years old) with different L1s (Chinese or Russian) but with the same L2 (Korean) and L3 (English). The participants completed truth-value judgment tasks designed to investigate their interpretation patterns for English sentences with negation and a quantifier (e.g., Tom did not cut all the trees). The results showed that both groups preferred the L3 interpretation similar to that preferred in their L2, but not in their L1, suggesting a potential L2 influence on L3 acquisition. The study evaluates L3 acquisition theories in light of these results.

Priming quantifier scope: Reexamining the evidence against scope inversion

In a study of quantifier-scope priming, Chemla and Bott (2015) found evidence suggesting that, while representations of quantifiers’ relative scope can be primed, a scope inversion operation cannot. We identify a confound in their materials. In Experiment 1, we replicate their finding with this confound intact. In Experiment 2, we remove the confound and find that all priming disappears. This confound demonstrates how structural priming paradigms can be sensitive to many dimensions of similarity, pointing to a need for task-specific controls. We conclude that the prior study does not provide evidence concerning the priming of either relative scope representations or operations. While priming of scope representations has been independently found in other paradigms, the jury is still out on Chemla and Bott’s more novel finding – the absence of priming of a scope inversion operation.

An investigation of numeral quantifiers in English

There exist a broad range of theories which model quantifier scope (Ruys & Winter 2011). The empirical coverage and predictions of three theories: Quantifier Raising (May 1985) with Scope Economy (Fox 2000), Feature Checking (Beghelli & Stowell 1997), and Choice Functions (Winter 1997) are tested using a sentence-picture verification task. Speakers rated the quality of sentences with bare and modified numeral quantifiers in surface and inverse scope conditions. In Experiment 1, it was discovered that bare numerals marginally resisted inverse scope, contra the predictions of (Beghelli & Stowell 1997). Experiment 2 revealed that the scope of numerals is clause-bound, in argument against the theory of Choice Functions which predict extra-clausal scope for existential quantifiers. The results suggest that a modified QR theory best accounts for the observed data.

Quantifier Scope in Russian

This paper documents certain quantifier scope ambiguities in Russian and argues that these are derived by means of a covert syntactic movement operation, Quantifier Raising (QR). By doing so, it argues against the popular “frozen scope” view of Russian (Ionin 2003) by showing that optional, non-local QR past vP level must be available in the language in exactly the contexts where it is available in English. Syntactic evidence for the parallelism comes from Inverse Linking, Antecedent Contained Deletion and other contexts that have been argued to point to the existence of QR in English. Additionally, evidence for the availability of subject Reconstruction for scope in Russian (contra Ionin 2003) strongly suggests that the mechanism deriving ambiguity in basic SVO sentences in Russian must involve subject Reconstruction plus object QR to vP, exactly as has been argued to be necessary for English in Johnson (2000; 2001). The conclusion that Russian possesses QR with the same properties known from English suggests that the availability of QR in certain languages or certain constructions should not be tied to the unavailability of Scrambling since Russian also exhibits Scrambling. This conclusion thus carries important implications for other languages still currently taken to be similarly scope frozen due to the availability of Scrambling.

A proof-theoretic approach to scope ambiguity in compositional vector space models

We investigate the extent to which compositional vector space models can be used to account for scope ambiguity in quantified sentences (of the form Every man loves some woman). Such sentences introduce one reading for each quantifier. We combine a polarised focussed sequent calculus for the non-associative Lambek Calculus NL as described in Moortgat and Moot (2011) with a non-compositional ap- proach to quantifier scope in vector space semantics introduced by Hedges and Sadrzadeh (2016) and (Sadrzadeh 2016). In particular, we obtain an automatic and compositional procedure for obtaining quantifier scope ambiguity in vector space models of meaning.

When is a Schema Not a Schema? On a Remark by Suszko

A 1971 paper by Roman Suszko, ‘Identity Connective and Modality’, claimed that a certain identity-free schema expressed the condition that there are at most two objects in the domain. Section 1 here gives that schema and enough of the background to this claim to explain Suszko’s own interest in it and related conditions—via non-Fregean logic, in which the objects in question are situations and the aim is to refrain from imposing this condition. Section 3 shows that the claim is false, and suggests a diagnosis as to why it might have been made, in terms of quantifier scope distinctions as they bear on schematic formulations. In between, Section 2 discusses an issue brought up by this discussion but not involving the mistaken claim itself, and shows that Suszko was familiar with two different ways (using identity) to set an upper or lower finite bound to the domain—a contrast which some contemporary readers may associate with David Lewis (for reasons that will be explained in that section).

A Principled Explanation on the Quantifier Scope Phenomena

The purpose of this study is to present a principled explanatory alternative mechanism for the scope puzzling phenomena in the quantifier constructions. For this, Multiple Agree (Chomsky 2001; Hiraiwa 2000), Phase (Chomsky 1998, 1999), Phase higher evaluation (Chomsky 1999), Feature-inheritance from Phase (Chomsky 2005, 2013, 2014), INT (Chomsky 1999, 2001) and semantic Duality of the Interface (Boeckx 2008; Chomsky 2005; Grohmann 2003; Kim 2018) are adopted. In addition, [±D]-feature is posited on the basis of the interpretation of θ–domain. By using this system, the DOC construction, the counterexample to Hornstein’s (1995, 1999) A-movement for Case-checking account, the counterexample to Fox’s (1995, 2000) Scope Economy account, and the bi-clausal quantifier sentence are solved. Not only that, the c-command and Fox’s (2000) Revised Modularity Hypothesis are also explained in a natural manner.

More free choice and more inclusion: An experimental investigation of free choice in nonmonotonic environments

Disjunctions in the scope of possibility modals give rise to a conjunctive inference, generally labeled 'free choice'. A prominent approach derives free choice as a kind of scalar implicature. In this paper, we focus on the predictions of two main type of accounts within this approach, with the goal of investigating what implicature-generating algorithm best captures free choice and related data. The first is based on a standard algorithm for computing implicatures, which proceeds by negating (or 'excluding') alternatives to a sentence and adding the information so obtained to the assertion. The second proceeds by directly conjoining alternatives to the assertion (or 'including' them). This paper provides evidence that discriminates between the exclusion and the inclusion accounts. We focus on sentences involving possibility modals and disjunctions in the scope of nonmonotonic quantifiers: our key example is "Exactly one girl cannot take Spanish or Calculus". We report on an inferential task experiment testing this case. We find clear evidence that the sentence has a free-choice-type reading, on which it suggests that one girl cannot take either Spanish or Calculus and all of the others can choose between the two. This is challenging for exclusion accounts, but in line with the predictions of inclusion accounts. This case constitutes, therefore, an argument for inclusion accounts.

Bare conditionals in the red

Bare conditionals, I argue, exhibit Conditional Duality in that when they appear in downward entailing environments they differ from bare conditionals elsewhere in having existential rather than universal force. Two recalcitrant phenomena are shown to find a new explanation under this thesis: bare conditionals under only, and bare conditionals in the scope of negative nominal quantifiers, or what has come to be known as Higginbotham’s puzzle. I also consider how bare conditionals behave when embedded under negation, arguing that such conditionals often involve denial negation. One important conclusion that emerges from the discussion is that an account of bare conditionals that validates Conditional Excluded Middle is not warranted. By limiting the scope of the (variably) strict analysis Conditional Duality is also a way of maintaining such an account.

Polarity sensitivity of question embedding: experimental evidence

Attitude predicates can be classified by the kinds of complements they can embed: declaratives, interrogatives or both. However, several authors have claimed that predicates like be certain can only embed interrogatives in specific environments. According to Mayr, these are exactly the environments that license negative polarity items (NPIs). In his analysis, both NPIs and embedded interrogatives are licensed by the same semantic strengthening procedure. If this is right, one would expect a correlation between acceptability of be certain whether and NPIs. The analysis also predicts a contrast between antecedents vs. consequents of conditionals and restrictors vs. scopes of universal quantifiers. This paper tests these predictions experimentally through an acceptability judgment task. We find that judgments for be certain whether do not correlate with judgments on NPIs, which suggests that be certain whether and NPIs are in fact licensed by different mechanisms.

Focus on Russian Scope: An Experimental Investigation of the Relationship between Quantifier Scope, Prosody, and Information Structure

An experimental investigation of quantifier scope in Russian SVO and OVS sentences, in which the factors of word order, prosody, information structure, and indefinite form are manipulated, shows that native Russian speakers have a preference for surface scope under neutral prosody, though this preference is more pronounced with odin ‘one’ indefinites than with dva ‘two’ indefinites. Furthermore, contrastive focus on the fronted object QP in OVS order is found to facilitate the inverse scope reading, but contrastive focus on the subject in SVO order is not. These findings have implications for the syntactic analysis of noncanonical word order in Russian ( Bailyn 2011 , Slioussar 2013 ) and support the link between contrastive focus and scope reconstruction in Russian ( Ionin 2003 , Neeleman and Titov 2009 ).

What do speaker judgments tell us about theories of quantifier scope in German?

In this paper we use German data to evaluate configurational and multi-factor approaches to quantifier scope. Configurational theories derive scope relations syntactically at the level of Logical Form; semantic and pragmatic factors are either built into the syntactic representation or ignored, at least during the first derivational step. By contrast, multi-factor approaches consider syntactic, semantic and pragmatic properties of quantifiers as multiple constraints affecting quantifier scope. We examined predictions for quantifier scope in German of the configurational theory by Frey (1993) and of the multi-factor account by Pafel (2005). These fundamentally different approaches were tested in a series of picture verification experiments to assess scope preferences in doubly quantified German sentences. The results show that at least three factors affect the preferred scope. Our findings are neither fully consistent with Frey’s configurational theory nor with Pafel’s multi-factor approach; both theories made incorrect predictions for German doubly quantified sentences with a subject-before-object word order. For object-before-subject sentences, however, the experimental data by and large support the predictions of Pafel’s (2005) multi-factor approach.

Scope marking and prosody in Hungarian

The paper presents an analysis of the results of three perception experiments that aimed to investigate the scope of postverbal quantifiers in Hungarian. These experiments found no correlations between wide vs. narrow scope readings of postverbal quantifiers and their stressed vs. unstressed pronunciations, contradicting a widespread assumption. In addition to the dominance of scope interpretation that corresponds to the linear order of constituents, previously unnoticed effects of the syntactic or thematic role of the postverbal quantifier and of the type of preverbal operator in the same sentence were found. These might indicate a more complex interaction of several factors or point to a greater role of extra-grammatical effects in determining the scope of quantifiers in Hungarian than previously assumed. The paper also addresses methodological issues that arise in the course of eliciting scope judgments experimentally.

How to Neutralize a Finite Clause Boundary: Phase Theory and the Grammar of Bound Pronouns

A bound pronoun in the subject position of a finite embedded clause renders the clause boundary relatively transparent to relations ordinarily confined to monoclausal, control, and raising configurations. For example, too/ enough-movement structures involving a finite clause boundary are degraded in sentences like * This book is too long [for John to claim [that Bill read ___ in a day]] but improved when the finite clause has a bound pronominal subject as in ? This book is too long [for John1to claim [that he1read ___ in a day]]. This bound pronoun effect holds across a wide range of phenomena including too/ enough-movement, tough-movement, gapping, comparative deletion, antecedent-contained deletion, quantifier scope interaction, multiple questions, pseudogapping, reciprocal binding, and multiple sluicing; we confirm the effect via a sentence acceptability experiment targeting some of these phenomena. Our account has two crucial ingredients: (a) bound pronouns optionally enter the derivation with unvalued ϕ-features and (b) phases are defined in part by convergence, so that under certain conditions, unvalued features void the phasal status of CP and extend the locality domain for syntactic operations.

Quantifier scope in sentence prosody?

Logical scope interpretation and sentence prosody exhibit intricate, yet scarcely studied interrelations across a variety of languages and constructions. Despite these observable interrelations, it is not clear whether quantifier scope by itself is able to directly affect prosodic form. Information structure is a key potential confounding factor, as it appears to richly interact both with scope interpretation and with prosodic form.To address this complication, the current study investigates, based on data from Hungarian, whether quantifier scope is expressed prosodically if information structure is kept in check. A production experiment is presented that investigates grammatically scope ambiguous doubly quantified sentences with varied focus structures, while lacking a syntactically marked topic or focus. In contrast to the information structural manipulation, which is manifest in the analysis of the acoustic data, the results reveal no prosodic effect of quantifier scope, nor the interaction of scope with information structure. This finding casts doubt on the notion that logical scope can receive direct prosodic expression, and it indirectly corroborates the restrictive view instead that scope interpretation is encoded in prosody only in cases in which it is a free rider on information structure.

The scope of children’s scope: Representation, parsing and learning

This paper reviews some developmental psycholinguistic literature on quantifier scope. I demonstrate how scope has been used as a valuable probe into children’s grammatical representations, the nature of children’s on-line understanding mechanisms, and the role that experience plays in language acquisition. First, children’s interpretations of certain scopally ambiguous sentences reveals that their syntactic representations are hierarchical, with the c-command relation playing a fundamental role in explaining interpretive biases. Second, children’s scope errors are explained by incremental parsing and interpretation mechanisms, paired with difficulty revising initial interpretations. Third, a priming manipulation reveals that children’s clauses, like those of adults, are represented with predicate-internal subjects. Finally, data on scope variation in Korean reveals that in the absence of disambiguating evidence, parameter setting is an essentially random process. Together, these discoveries reveal how the developmental psycholinguistics of scope has proved a valuable tool for probing issues of grammar, parsing and learning.

The Quest for Simplicity of Quantifier Scope Interaction

The Quest for Simplicity of Quantifier Scope Interaction

Interpreting presuppositions in the scope of quantifiers: "every" vs. "at least one"

This paper experimentally investigates presupposition projection from the scope ofthe quantifiers every and at least one, as triggered by the factive verb be aware and the iterativeadverb again. The first issue we are concerned with is whether presuppositions projectuniversally or existentially from quantified sentences. Different theoretical accounts endorseopposing views here (e.g., Heim, 1983; Geurts, 1999; Beaver, 2001; Schlenker, 2008, 2009;Fox, 2012), while recent experimental work (Chemla, 2009; Tiemann, 2014) suggests thatthe force of the projected presupposition varies by quantifier. The second issue we look atis how the descriptively observed readings arise—in particular, as a direct result output fromthe projection mechanism, or via additional, independent mechanisms such as domain restriction(e.g., Geurts and van Tiel, 2016): if the domain of the quantifier is restricted, this canyield what looks like non-universal inferences in light of the overall, unrestricted domain, evenif the projection mechanism itself yields a universal presupposition. Finally, we test whetherthe presupposed content also forms part of the entailed content, at least for certain triggers(Sudo, 2012; Klinedinst, 2016; Zehr and Schwarz, 2016). Our results yield clearly differentpatterns for every and at least one, with every giving rise to universal presuppositions, which,to a very limited extent, can be weakened by domain restriction, and at least one overwhelminglygiving rise to non-universal presuppositions. Our results also indicate the availability ofpresupposition-less readings for both triggers in the task at hand, apparently more prevalentthan domain restriction. Thereby, we present novel evidence that helps to pinpoint which of thetheoretical options can be substantiated experimentally.Keywords: Presupposition projection, quantifiers, domain restriction, entailment.

Heuristics in Language Comprehension

We used a sentence-picture matching task to demonstrate that heuristics can influence language comprehension. Interpretation of quantifier scope ambiguous sentences such as Every kid climbed a tree was investigated. Such sentences are ambiguous with respect to the number of trees inferred; either several trees were climbed or just one. The availability of the NOUN VERB NOUN (N-V-N) heuristic, e.g., KID CLIMB TREE, should contribute to the interpretation of how many trees were climbed. Specifically, we hypothesized that number choices for these stimuli would be predicted by choices previously made to corresponding (full) sentences. 45 participants were instructed to treat N-V-N triplets such as KID CLIMB TREE as telegrams and select a picture, regarding the quantity (“several” vs. “one”) associated with tree. Results confirmed that plural responses to quantifier scope ambiguous sentences significantly predict increased plural judgments in the picture-matching task. This result provides empirical evidence that the N-V-N heuristic, via conceptual event knowledge, can influence sentence interpretation. Furthermore, event knowledge must include the quantity of participants in the event (especially in terms of “several” vs. “one”). These findings are consistent with our model of language comprehension functioning as “Heuristic first, algorithmic second.” Furthermore, results are consistent with judgment and decision making in other cognitive domains.