Quantifying quantifier representations: Experimental studies, computational modeling, and individual differences
Sonia Ramotowska

Abstract:
This thesis proposes a new, cognitive perspective on the meaning representations and verification of natural language quantifiers. According to the traditional, logical view, quantity words are represented in the form of truth conditions shared across language users. However, a growing body of evidence shows variability among speakers in semantic representations and verification strategies of quantifies. The logical view cannot explain the individual differences in meaning representations of quantity words.
In contrast, according to the cognitive perspective, the truth-conditional representations of quantifiers may vary between speakers. Moreover, the model captures the properties of quantifiers such as vagueness and polarity.
Computational models play a key role in the investigation of meaning representations. This thesis presents three computational models. Each model captures different aspects of the representation and verification of quantified sentences, for example, the quantifier’s truth condition, vagueness, or processing stages. Moreover, computational models disentangle the formal properties of quantifiers from individual differences in task performance.
Chapter 2 investigates the individual differences in meaning representations of five natural language quantifiers: few, many, most, fewer than half, and more than half. By using the computational model, we capture two key properties of quantifier meaning – truth conditions, vagueness – as well as variation in the task performance (response errors) of participants. The results of cluster analysis show that participants constitute three groups with different thresholds for few, many, and most. Moreover, the groups differ in the perception of the vagueness of quantifiers, and they put quantifiers in a different order on a mental line.
Chapter 3 further extends the findings of Chapter 2. By using another computational model, we investigate the meaning representations and verification of most and more than half. The results of Chapter 3 show that most is sensitive to individual differences in representations and its verification is proportion-dependent. In addition, despite the individual differences in meanings, the meaning
representations are stable over time. 
Positive quantifiers (e.g., more than half ) are processed faster than their negative counterparts. In Chapter 4, we use computational model to test the predictions of two competing accounts (pragmatic and two-step models) explaining the polarity effect. Two quantifier verification experiments and modeling data show two separate sources of polarity effect. In conclusion, the findings support both
pragmatic and two-step accounts.
Chapter 5 further investigates the source of the polarity effect by directly testing the predictions of the two-step model. The two-step model postulates that the negative quantifiers are verified slower because they require and extra processing step compared to positive quantifiers. Chapter 5 presents the results of the electroencephalography picture-sentence verification experiment with two quantifiers: fewer than half and more than half. We used computational model to estimate and compare the number of processing stages of the quantified sentences. The findings of Chapter 5 challenge the two-step model.
Chapter 6 investigates one of the explanations of the semantic universals, namely the learnability hypothesis. In a large-scale experiment, we test the speed of acquisition of eight different quantifiers that vary in three formal properties: monotonicity, conservativity, and quantity. The findings of Chapter 6 support the learnability explanation of some of the semantic universals. Moreover, Chapter 6 stresses methodological aspects of experimental investigation of semantic universals.