Fabian Schlotterbeck

Easy Solutions for a Hard Problem? The Computational Complexity of Reciprocals with Quantificational Antecedents

We report two experiments which tested whether cognitive capacities are limited to those functions that are computationally tractable (PTIME-Cognition Hypothesis). In particular, we investigated the semantic processing of reciprocal sentences with generalized quantifiers, i.e., sentences of the form Q dots are directly connected to each other, where Q stands for a generalized quantifier, e.g. all or most. Sentences of this type are notoriously ambiguous and it has been claimed in the semantic literature that the logically strongest reading is preferred (Strongest Meaning Hypothesis). Depending on the quantifier, the verification of their strongest interpretations is computationally intractable whereas the verification of the weaker readings is tractable. We conducted a picture completion experiment and a picture verification experiment to investigate whether comprehenders shift from an intractable reading to a tractable reading which should be dispreferred according to the Strongest Meaning Hypothesis. The results from the picture completion experiment suggest that intractable readings occur in language comprehension. Their verification, however, rapidly exceeds cognitive capacities in case the verification problem cannot be solved using simple heuristics. In particular, we argue that during verification, guessing strategies are used to reduce computational complexity.

The Processing Domain of Scope Interaction

We present six experiments which investigated the time course of the interpretation of quantifier scope ambiguity. We used variable binding in the first quantifier to enforce scope inversion. The first two experiments were offline tests that established that the sentences had the proposed interpretations. The third experiment employed self-paced reading to show that potential difficulty in doubly quantified sentences with a variable is not due to interpreting the variable per se, but must come from scope inversion. We then report the results of two further self-paced reading experiments and an experiment in which we measured eye-movements during reading. Taken together, the reading time studies demonstrate that relative scope is only computed at the sentence-boundary. Only at the end of the sentence we found clear scope inversion effects. Our study shows that quantifier scope is not assigned incrementally, but depends on a complete minimal sentence.

Embedded Scalars, Preferred Readings and Prosody: An Experimental Revisit

The scalar item some is widely assumed to receive a meaning enrichment to some but not all if it occurs in matrix position. The question under which circumstances this enrichment can occur in certain embedded positions plays an important role in deciding how to delineate semantics and pragmatics. We present new experimental data that bear on this theoretical issue. In distinction to previous experimental approaches, we presented sentence material auditorily in order to explicitly control prosodic markedness of the scalar item. Moreover, our experiment sheds light on the relative preferences or salience of candidate readings. The presented data turn out to be unexpected under a traditional Gricean view, but also challenge the idea of disambiguation by logical strength in grammaticalist approaches.

Turning Adults into Children: Evidence for Resource-Based Accounts of Errors with Universal Quantification

The present study shows that adults make errors of quantifier spreading similar to those commonly observed in preschool children when interpreting universally quantified sentences. In a resource demanding version of the truth value judgment task, adult participants often rejected scope disambiguated, universally quantified sentences (e.g. Every kid is such that it was praised by exactly one teacher) in situations where each kid was praised by exactly one teacher, but there was (A) an additional teacher praising no kids (= classic quantifier spreading) and/or (B) a teacher who praised more than one kid. While the classic spreading error has been studied extensively, spreading errors of the second type have not been attested in the acquisition literature. Neither type of error occurred in an ordinary picture verification task using the same materials. A third experiment ruled out the possibility that the errors observed in Experiment 1 are due to misrepresenting the situations in memory. Our results are most consistent with resource-based accounts of quantifier spreading (e.g. Geurts in Lang Acquis 11:197–218, 2003) but are unexpected under the discontinuity hypothesis (e.g. Philip in Event quantification in the acquisition of universal quantification. UMI, Ann Arbor, Michigan 1995) and accounts relying on plausible dissent (e.g. Crain et al. in Lang Acquis 5:83–153, 1996). We outline a novel explanation of quantifier spreading in terms of the computation and evaluation of default models that can account for the presented results as well as earlier findings reviewed in the introduction of the chapter.

From truth conditions to processes: how to model the processing difficulty of quantified sentences based on semantic theory

The present dissertation is concerned with the processing difficulty of quantified sentences and how it can be modeled based on semantic theory. Processing difficulty of quantified sentences is assessed using psycholinguistic methods such as systematically collecting truthvalue judgments or recording eye movements during reading. Predictions are derived from semantic theory via parsimonious processing assumptions, taking into account automata theory, signal detection theory and computational complexity. Chapter 1 provides introductory discussion and overview. Chapter 2 introduces basic theoretical concepts that are used throughout the rest of the dissertation. In chapter 3, processing difficulty is approached on an abstract level. The difficulty of the truth evaluation of reciprocal sentences with generalized quantifiers as antecedents is classified using computational complexity theory. This is independent of the actual algorithms or procedures that are used to evaluate the sentences. One production and one sentence-picture verification experiment are reported which tested whether cognitive capacities are limited to those functions that are computationally tractable. The results indicate that intractable interpretations occur in language comprehension but also that their verification rapidly exceeds cognitive capacities in case the verification problem cannot be solved using simple heuristics. Chapter 4 discusses two common approaches to model the canonical verification procedures associated with quantificational sentences. The first is based on the semantic automata model which conceives of quantifiers as decision problems and characterizes the computational resources that are needed to solve them. The second approach is based on the interface transparency thesis, which stipulates a transparent interface between semantic representations and the realization of verification procedures in the general cognitive architecture. Both approaches are evaluated against experimental data. Chapter 5 focuses on a test case that is challenging for both of these approaches. In particular, increased processing difficulty of more than n as compared to fewer than n is investigated. A processing model is proposed which integrates insights from formal semantics with models from cognitive psychology. This model can be seen as im-