The processing of polar quantifiers, and numerosity perception

Questions About Quantifiers: Symbolic and Nonsymbolic Quantity Processing by the Brain

One approach to understanding how the human cognitive system stores and operates with quantifiers such as "some," "many," and "all" is to investigate their interaction with the cognitive mechanisms for estimating and comparing quantities from perceptual input (i.e., nonsymbolic quantities). While a potential link between quantifier processing and nonsymbolic quantity processing has been considered in the past, it has never been discussed extensively. Simultaneously, there is a long line of research within the field of numerical cognition on the relationship between processing exact number symbols (such as "3" or "three") and nonsymbolic quantity. This accumulated knowledge can potentially be harvested for research on quantifiers since quantifiers and number symbols are two different ways of referring to quantity information symbolically. The goal of the present review is to survey the research on the relationship between quantifiers and nonsymbolic quantity processing mechanisms and provide a set of research directions and specific questions for the investigation of quantifier processing.

Uncovering the Structure of Semantic Representations Using a Computational Model of Decision-Making

According to logical theories of meaning, a meaning of an expression can be formalized and encoded in truth conditions. Vagueness of the language and individual differences between people are a challenge to incorporate into the meaning representations. In this paper, we propose a new approach to study truth-conditional representations of vague concepts. For a case study, we selected two natural language quantifiers most and more than half. We conducted two online experiments, each with 90 native English speakers. In the first experiment, we tested between-subjects variability in meaning representations. In the second experiment, we tested the stability of meaning representations over time by testing the same group of participants in two experimental sessions. In both experiments, participants performed the verification task. They verified a sentence with a quantifier (e.g., "Most of the gleerbs are feezda.") based on the numerical information provided in the second sentence, (e.g., "60% of the gleerbs are feezda"). To investigate between-subject and within-subject differences in meaning representations, we proposed an extended version of the Diffusion Decision Model with two parameters capturing truth conditions and vagueness. We fit the model to responses and reaction times data. In the first experiment, we found substantial between-subject differences in representations of most as reflected by the variability in the truth conditions. Moreover, we found that the verification of most is proportion-dependent as reflected in the reaction time effect and model parameter. In the second experiment, we showed that quantifier representations are stable over time as reflected in stable model parameters across two experimental sessions. These findings challenge semantic theories that assume the truth-conditional equivalence of most and more than half and contribute to the representational theory of vague concepts. The current study presents a promising approach to study semantic representations, which can have a wide application in experimental linguistics.

The semantically annotated corpus of Polish quantificational expressions

The paper presents a manually annotated corpus of Polish quantificational expressions. The quantifier annotation was conducted on top of existing gold-stan/dard data for Polish as its separate layer. This paper releases the data and gives an overview of the corpus and related tools. As far as we know, this is the first large-scale annotation of generalized quantifiers together with their crucial semantic properties, including monotonicity profile. We also discuss the potential further use of the corpus in linguistics and cognitive science.

The influence of polarity items on inferential judgments

Polarity items are linguistic expressions such as any, at all, some, which are acceptable in some linguistic environments but not others. Crucially, whether a polarity item is acceptable in a given environment is argued to depend on the inferences (in the reasoning sense) that this environment allows. We show that the inferential judgments reported for a given environment are modified in the presence of polarity items. Hence, there is a two-way influence between linguistic and reasoning abilities: the linguistic acceptability of polarity items is dependent on reasoning facts and, conversely, reasoning judgments can be altered by the mere addition of seemingly innocuous polarity items.

Negative polarity in quantifiers evokes greater activation in language-related regions compared to negative polarity in adjectives

The processing of sentences with negative quantifiers (e.g., few) is more costly than of sentences that contain their positive counterparts (e.g., many). While this polarity effect is robust and reliably replicable, its neurological bases are not well understood. In this study, we use functional magnetic resonance imaging (fMRI) paradigm for 30 participants to assess the polarity effect in sentences with polar quantifiers, and compare it with the polarity effect of polar adjectives. Both in quantifiers and in adjectives, the polarity effect manifests in the anterior insula bilaterally. The polarity effect in quantifiers, however, shows greater activation in the left hemisphere than it does for adjectives. In particular, left inferior frontal gyrus (IFG) and left superior temporal sulcus (STS) show increased activation for polarity in quantifiers than in adjectives, which is the evidence for the specific involvement of the language network in this type of polarity processing. Using the polarity effect in adjectives as a control, we provide further evidence for the linguistic complexity that negative quantifiers implicate on processing.

Context and Complexity in Incremental Sentence Interpretation: An ERP Study on Temporal Quantification

The present event-related potential (ERP) study used picture-sentence verification to investigate the neurolinguistic correlates of the online processing of compositional-semantic information. To this end, we examined context effects on sentences involving temporal adverbial quantification likeJana war jeden Morgen schwimmen an den Arbeitstagen ("Jana went for a swim every morning during the working week"). We tested whether the conceptual complexity associated with quantifying over time intervals leads to delayed predictions regarding the upcoming words in a sentence. The present study replicated previous results relating to quantification over individuals, which are conceptually less complex than time intervals. Analogous to previous studies, false vs. true sentences elicited an N400 whenever contextual cues did not permit a potential revision of a locally assigned truth value. The present results are compatible with an approach under which contextual cues are immediately considered for predicting how a sentence continues. The fact that the contextual complexity did not lead to processing delays indicates that the processing system quickly abstracts away from the conceptual complexity associated with the linguistic input if such an abstraction is possible.

Memory Load Effect in the Real-Time Processing of Scalar Implicatures

This study examines effects of memory load on the processing of scalar implicature via a dual-task paradigm using reading span and self-paced reading. Results indicate that participants showed online sensitivity to underinformative sentences (e.g., Some birds have wings and beaks) at the end of the sentence. This online sensitivity disappeared when participants were under increased memory load. Moreover, participants in the memory-load condition did not show sensitivity to semantically false sentences (e.g., All books have pictures and drawings). These results pose important conceptual and methodological questions of (1) whether the processing cost associated with scalar implicatures can be attributed to general proposition evaluation rather than scalar implicature derivation per se (Bale et al. in Semant Linguist Theory 20:525-543, 2010), and (2) to what degree memory load affects implicature computation only. I conclude with a discussion of these two issues for future research.

So Many Are "Few," but so Few Are Also "Few" - Reduced Semantic Flexibility in bvFTD Patients

The processing of quantifier words such as "many" or "few" is a complex operation supported by a plastic fronto-parietal network predominantly in the left hemisphere. The internal reference criterion defining a quantifier (e.g., ≥50% for "many") can be modified in a learning paradigm. Most interestingly, changing the criterion for one quantifier also leads to a change in the criterion for the untrained quantifier, i.e., a semantic restructuring effect, which is supported by Broca's region in the left inferior frontal cortex. Here, we applied this paradigm to patients with the behavioral variant of fronto-temporal dementia (bvFTD) because they suffer from loss of cognitive flexibility, reduced ability to process quantities and their values, impaired reinforcement learning, and language comprehension deficits. The question was whether the patients would be able to perform the task, show direct learning of the new quantifier meanings, and exhibit cognitive flexibility in terms of semantic restructuring. Eleven bvFTD patients took part in two behavioral experiments. In Experiment 1, in a first baseline block, each individual's criterion for "many" and "few" was assessed. In block 2, subjects received feedback about their decisions. Contrary to their initial notion, a proportion of 40% yellow circles was reinforced as "many." In block 3, the effect of this training on their judgments of "many" and "few" was re-assessed. The group of bvFTD patients showed a learning effect for the new criterion trained for the quantifier "many," but failed to generalize this criterion shift to the other quantifier "few." Experiment 2 was similar to Experiment 1, but the patients were trained in Block 2 to judge 60% of circles as "few," with no training for "many." Again, there was an average learning effect for the trained quantifier "few" over the entire group, but no generalization to "many." Since the patients were still able to perform the task and showed learning of "many" to direct feedback, the data suggest that the generalization process, rather than initial learning, is more vulnerable to fronto-temporal degeneration.

"Few" or "Many"? An Adaptation Level Theory Account for Flexibility in Quantifier Processing

Quantifiers (e.g., “many,” “some,” “at least seven,” “more than half”) are words characterizing amounts or numerosities by reference to an internal threshold, or degree. For some quantifiers, this degree is not uniquely defined: It varies for external contexts (“many lions”/“many flies”) but may also be shifted within an individual (“many fries” for a hungry/full person). Previous studies showed that manipulation of the degree for one quantifier can impact that of other quantifiers. In this study, we tested whether such changes can occur by mere habituation, as formalized in the Adaptation Level Theory by Helson (1948) for sensory stimuli such as brightness or weight. To this end, participants read a quantifier statement and then judged whether a visual display with varying amounts (20–80%) of blue and yellow circles matched that statement. In Block 1, we identified which proportion of circles of a given color was judged by participants as “many” or “few.” In Block 2, we modified the presentation of stimuli such that (1) only the quantifier “many” was used and (2) only low proportions of circles of a given color were presented, thus changing the base rate at which proportions were encountered together with “many.” The hypothesis was that the internal degree of what is interpreted as “many” would be shifted downward and that this shift would also affect judgments of “few.” Block 3 was identical to Block 1, serving as a test for the expected effect on the degree/threshold for/across all proportions. The findings were as expected: The probability of accepting 40% as “many” was increased during Block 2, indicating adaptation. Likewise, the probability function for “few” was shifted in a parallel fashion around the proportion 40%. These findings complemented earlier studies demonstrating intra-individual flexibility in quantifier processing. They show that this flexibility can even be observed in the absence of explicitly stated verbal contexts or reinforcements, in line with the Adaptation Level Theory formulated originally for magnitudes, i.e., non-linguistic representations of quantities.

Logical negation mapped onto the brain

High-level cognitive capacities that serve communication, reasoning, and calculation are essential for finding our way in the world. But whether and to what extent these complex behaviors share the same neuronal substrate are still unresolved questions. The present study separated the aspects of logic from language and numerosity-mental faculties whose distinctness has been debated for centuries-and identified a new cytoarchitectonic area as correlate for an operation involving logical negation. A novel experimental paradigm that was implemented here in an RT/fMRI study showed a single cluster of activity that pertains to logical negation. It was distinct from clusters that were activated by numerical comparison and from the traditional language regions. The localization of this cluster was described by a newly identified cytoarchitectonic area in the left anterior insula, ventro-medial to Broca's region. We provide evidence for the congruence between the histologically and functionally defined regions on multiple measures. Its position in the left anterior insula suggests that it functions as a mediator between language and reasoning areas.

Probing the mental representation of quantifiers

In this study, we investigate the mental representation of non-numerical quantifiers ("some", "many", "all", etc.) by comparing their use in abstract and in grounded perceptual contexts. Using an approach similar to that used in the number domain, we test whether (and to what extent) such representation is constrained by the way we perceive the world through our senses. In two experiments, subjects either judged the similarity of quantifier pairs (presented as written words) or chose among a predetermined list of quantifiers the one that best described a visual image depicting a variable number of target and non-target items. The results were rather consistent across experiments, and indicated that quantifiers are mentally organized on an ordered but non-linear compressed scale where the quantifiers that imply small quantities appear more precisely differentiated across each other compared to those implying large quantities. This fits nicely with the idea that we construct our representations of such symbols mainly by mapping them to the representations of quantities that we derive from perception.

Neural correlates of fine-grained meaning distinctions: An fMRI investigation of scalar quantifiers

Communication involves successfully deriving a speaker's meaning beyond the literal expression. Using fMRI, it was investigated how the listener's brain realizes distinctions between enrichment-based meanings and literal semantic meanings. The neural patterns of the Mandarin scalar quantifier you-de (similar to some in English) which implies the meanings not all and not most via scalar enrichment, with the specific quantifier shao-shu-de (similar to less than half in English) which lexico-semantically encodes the meanings not all and not most, were compared. Listeners heard sentences using either quantifier, paired with pictures in which either less than half, more than half, or all of the people depicted in the picture were doing the described activity; thus, the conditions included both implicature-based and semantics-based picture-sentence mismatches. Imaging results showed bilateral ventral IFG was activated for both kinds of mismatch, whereas basal ganglia and left dorsal IFG were activated uniquely for implicature-based mismatch. These findings suggest that resolving conflicts involving inferential aspects of meaning employs different neural mechanisms than the processing based on literal semantic meaning, and that the dorsal prefrontal/basal ganglia pathway makes a contribution to implicature-based interpretation. Furthermore, within the implicature-based conditions, different neural generators were implicated in the processing of strong implicature mismatch (you-de in the context of a picture in which "all" would have been true) and weak implicature mismatch (you-de in the context of a picture in which "most" would have been true), which may have important implications for theories of pragmatic comprehension. Hum Brain Mapp 38:3848-3864, 2017. © 2017 Wiley Periodicals, Inc.

Cross-linguistic patterns in the acquisition of quantifiers

Learners of most languages are faced with the task of acquiring words to talk about number and quantity. Much is known about the order of acquisition of number words as well as the cognitive and perceptual systems and cultural practices that shape it. Substantially less is known about the acquisition of quantifiers. Here, we consider the extent to which systems and practices that support number word acquisition can be applied to quantifier acquisition and conclude that the two domains are largely distinct in this respect. Consequently, we hypothesize that the acquisition of quantifiers is constrained by a set of factors related to each quantifier's specific meaning. We investigate competence with the expressions for "all," "none," "some," "some…not," and "most" in 31 languages, representing 11 language types, by testing 768 5-y-old children and 536 adults. We found a cross-linguistically similar order of acquisition of quantifiers, explicable in terms of four factors relating to their meaning and use. In addition, exploratory analyses reveal that language- and learner-specific factors, such as negative concord and gender, are significant predictors of variation.