Quantifier Scope Ambiguities Research Articles

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.

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.

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.

Quantifier Scope in Categorical Compositional Distributional Semantics

In previous work with J. Hedges, we formalised a generalised quantifiers theory of natural language in categorical compositional distributional semantics with the help of bialgebras. In this paper, we show how quantifier scope ambiguity can be represented in that setting and how this representation can be generalised to branching quantifiers.

Introducing Continuations

This working paper introduces CONTINUATIONS (a concept borrowed from computer science) as a new technique for characterizing certain aspects of the semantics of a natural language. I should emphasize at the outset that this is just an introduction, and that more a rigorous and thorough treatment is under development (see Barker (ms)). In the meantime, this paper mentions certain formal results without proving them, and describes certain new empirical generalizations without exploring them. What it will do is provide an explicit account of a range of familiar phenomena relat­ed to quantification, including quantifier scope ambiguity, NP as a scope island, and generalized coordination. What makes the account noteworthy is that it provides a fully and strictly compositional analysis of quantification and generalized coordina­tion that does not rely on syntactic movement operations such as Quantifier Move­ment, auxiliary storage mechanisms such as Cooper Storage, or type ambiguity as in Hendriks' Flexible Types system.

Quantifier Scope Ambiguity and Definiteness

Proceedings of the Ninth Annual Meeting of the Berkeley Linguistics Society (1983), pp. 25-36

Quantifier Scope Ambiguity and Definiteness

Proceedings of the Ninth Annual Meeting of the Berkeley Linguistics Society (1983), pp. 25-36

Agnostic hyperintensional semantics

A hyperintensional semantics for natural language is proposed which is agnostic about the question of whether propositions are sets of worlds or worlds are (maximal consistent) sets of propositions. Montague’s theory of intensional senses is replaced by a weaker theory, written in standard classical higher-order logic, of fine-grained senses which are in a many-to-one correspondence with intensions; Montague’s theory can then be recovered from the proposed theory by identifying the type of propositions with the type of sets of worlds and adding an axiom to the effect that each world is the set of propositions which are true there. Senses are compositionally assigned to linguistic expressions by a categorial grammar with only two rule schemas, based on the implicative fragment of intuitionistic linear propositional logic, and a fully explicit grammar fragment is provided that illustrates the compositional assignment of sense to a variety of constructions, including dummy-subject constructions, infinitive complements, predicative adjectives and nominals, raising to subject, ‘tough-movement’, and quantifier scope ambiguities. Notably, the grammar and the derivations that it licenses never make reference to either worlds or to the extensions of senses.

Interpreting Quantifier Scope Ambiguity: Evidence of Heuristic First, Algorithmic Second Processing

The present work suggests that sentence processing requires both heuristic and algorithmic processing streams, where the heuristic processing strategy precedes the algorithmic phase. This conclusion is based on three self-paced reading experiments in which the processing of two-sentence discourses was investigated, where context sentences exhibited quantifier scope ambiguity. Experiment 1 demonstrates that such sentences are processed in a shallow manner. Experiment 2 uses the same stimuli as Experiment 1 but adds questions to ensure deeper processing. Results indicate that reading times are consistent with a lexical-pragmatic interpretation of number associated with context sentences, but responses to questions are consistent with the algorithmic computation of quantifier scope. Experiment 3 shows the same pattern of results as Experiment 2, despite using stimuli with different lexical-pragmatic biases. These effects suggest that language processing can be superficial, and that deeper processing, which is sensitive to structure, only occurs if required. Implications for recent studies of quantifier scope ambiguity are discussed.

Bias of quantifier scope interpretation is attenuated in normal aging and semantic dementia

Many sentences with two quantifiers exhibit a phenomenon known as “quantifier scope ambiguity.” Consider the example A unicorn ran through every garden, which contains the quantifiers “a” and “every.” Most speakers of English agree that it may refer to one or more than one unicorn. Very little previous work has evaluated the ability of brain-damaged or aphasic patients to interpret such sentences. We administered a sentence-reading task with picture verification to a group of semantic dementia patients ( N = 5) and a matched group of cognitively normal controls ( N = 23). Controls exhibited a tendency to interpret the word every as having wide scope regardless of the order of quantifiers, as evidenced by decreased reaction time and increased accuracy when verifying pictures that required this interpretation. This bias was attenuated by increasing age and by the presence of semantic dementia. Furthermore, higher FAS fluency scores were associated with slower responses and more errors, while higher semantic fluency scores were associated with the opposite pattern. These findings fit best with a model in which the initial products of linguistic analysis are underspecified and biases in their interpretation arise subsequently through frontally mediated logical or pragmatic reasoning.

The neural underpinnings of semantic ambiguity and anaphora

We used event-related brain potentials (ERPs) in order to investigate how definite NP anaphors are integrated into semantically ambiguous contexts. Although sentences such as Every kid climbed a tree lack any syntactic or lexical ambiguity, these structures exhibit two possible meanings, where either many trees or only one tree was climbed. This semantic ambiguity is the result of quantifier scope ambiguity. Previous behavioural studies have shown that a plural definite NP continuation is preferred (as reflected in a continuation sentence, e.g., The trees were in the park) over singular NPs (e.g., The tree was in the park). This study aimed to identify the neurophysiological pattern associated with the integration of the continuation sentences, as well as the time course of this process. We examined ERPs elicited by the noun and verb in continuation sentences following ambiguous and unambiguous context sentences. A sustained negative shift was most evident at the Verb position in sentences exhibiting scope ambiguity. Furthermore, this waveform did not differentiate itself until 900 ms after the presentation of the Noun, suggesting that the parser waits to assign meaning in contexts exhibiting quantifier scope ambiguity, such that such contexts are left as underspecified representations.

Competition During the Processing of Quantifier Scope Ambiguities: Evidence from Eye Movements during Reading

We investigated the processing of sentences containing a quantifier scope ambiguity, such as Kelly showed a photo to each critic, which is ambiguous between the indefinite phrase (a photo) having one or many referents. Ambiguity resolution requires the computation of relative quantifier scope, with either a photo or each critic taking wide scope, thereby determining the number of referents. Using eye tracking, we established that multiple factors, including the grammatical function and surface linear order of quantified phrases, along with their lexical characteristics, interact during the processing of relative quantifier scope, with conflict between factors incurring a processing cost. We discuss the results in terms of theoretical accounts attributing sentence-processing difficulty to either reanalysis (e.g., Fodor, 1982) or competition between rival analyses (e.g., Kurtzman & MacDonald, 1993).

The Elusive Scope of Descriptions

AbstractSentences with more than one quantifier often exhibit ambiguities. For example, ‘Every miner went to a meeting’ has two readings depending on whether we take there to be one meeting that every miner went to or (possibly) different meetings corresponding to each miner. This paper discusses the theory that such ambiguities are directly akin to quantifier scope ambiguities in logic. Certain syntactic and semantic evidence suggests that with indefinite and definite descriptions, such as ‘a meeting’ and ‘the president’, these ambiguities are better understood in some other way, either as being due to quantifier domain restrictions or choice functions. This paper discusses the major considerations in this debate by way of an introduction to the type of research being conducted at the intersection of linguistics and philosophy of language.

The Role of Context in the Resolution of Quantifier Scope Ambiguities

This paper presents experimental results that elucidate some aspects of semantic processing, i.e. of the system that allows perceivers to associate an interpretation to a sentence on‐line. The phenomenon under investigation is the resolution of quantifier scope ambiguities. Sentences containing multiple quantifiers (i.e. everybody, some musician, etc.) are known to give rise to several interpretations. The question addressed in this work is how this kind of ambiguity is resolved in the on‐line process of constructing an interpretation for a sentence. The research reported here concentrates exclusively on English and French interrogative sentences, and in particular on the case of ambiguous how many questions that contain a universally quantified subject, every N. The central results of this paper are the following. First, quantifier scope preferences are shown to be problematic for the most straightforward extension of an economy‐based model to the processing of meaning, as evidenced by questionnaire studies in English and in French. Second, a model is elaborated in which the attested scope preferences are determined by the interaction with context. The results from a self‐paced reading study in English indicate that context plays a crucial role in the processing of scope ambiguity. Third, while incremental context interactive models have been claimed to induce immediate resolution of structural ambiguity (Crain & Steedman 1985; Altmann & Steedman 1988; and others), it is argued here that the interaction with context can also delay such ambiguity resolution, as evidenced by the results of the English self‐paced reading study. Finally, comparison of the two languages, English and French, sheds further light onto the phenomenon under investigation.

Factoring Predicate Argument and Scope Semantics: Underspecified Semantics with LTAG

In this paper we propose a compositional semantics for lexicalizedtree-adjoining grammar (LTAG). Tree-local multicomponent derivationsallow separation of the semantic contribution of a lexical item into onecomponent contributing to the predicate argument structure and a secondcomponent contributing to scope semantics. Based on this idea asyntax-semantics interface is presented where the compositionalsemantics depends only on the derivation structure. It is shown that thederivation structure (and indirectly the locality of derivations) allowsan appropriate amount of underspecification. This is illustrated byinvestigating underspecified representations for quantifier scopeambiguities and related phenomena such as adjunct scope and islandconstraints.

Glue semantics for HPSG

‎The glue approach to semantic interpretation has been developed principally for Lexical Functional Grammar. Recent work has shown how glue can be used with a variety of syntactic theories and this paper outlines how it can be applied to HPSG. As well as providing an alternative form of semantics for HPSG, we believe that the benefits of HPSG glue include the following: (1) simplification of the Semantics Principle; (2) a simple and elegant treatment of modifier scope, including empirical phenomena like quantifier scope ambiguity, the interaction of scope with raising, and recursive modification; (3) an analysis of control that handles agreement between controlled subjects and their coarguments while allowing for a property denotation for the controlled clause; (4) re-use of highly efficient techniques for semantic derivation already implemented for LFG, and which target problems of ambiguity management also addressed by Minimal Recursion Semantics.

Introducing Continuations

This working paper introduces CONTINUATIONS (a concept borrowed from computer science) as a new technique for characterizing certain aspects of the semantics of a natural language. I should emphasize at the outset that this is just an introduction, and that more a rigorous and thorough treatment is under development (see Barker (ms)). In the meantime, this paper mentions certain formal results without proving them, and describes certain new empirical generalizations without exploring them. What it will do is provide an explicit account of a range of familiar phenomena relat­ed to quantification, including quantifier scope ambiguity, NP as a scope island, and generalized coordination. What makes the account noteworthy is that it provides a fully and strictly compositional analysis of quantification and generalized coordina­tion that does not rely on syntactic movement operations such as Quantifier Move­ment, auxiliary storage mechanisms such as Cooper Storage, or type ambiguity as in Hendriks' Flexible Types system.

Plausible Reasoning and the Resolution of Quantifier Scope Ambiguities

Despite overwhelming evidence suggesting that quantifier scope is a phenomenon that must be treated at the pragmatic level, most computational treatments of scope ambiguities have thus far been a collection of syntactically motivated preference rules. This might be in part due to the prevailing wisdom that a commonsense inferencing strategy would require the storage of and reasoning with a vast amount of background knowledge. In this paper we hope to demonstrate that the challenge in developing a commonsense inferencing strategy is in the discovery of the relevant commonsense data and in a proper formulation of the inferencing strategy itself, and that a massive amount of background knowledge is not always required. In particular, we present a very effective procedure for resolving quantifier scope ambiguities at the pragmatic level using simple ‘quantitative’ data that is readily available in most database environments.