Inferential patterns of generalized quantifiers and their applications to scalar reasoning

Abstract

This thesis studies the inferential patterns of generalized quantifiers (GQs) and their applications to scalar reasoning. In Chapter 1, I introduce the basic notions of Generalized Quantifier Theory (GQT) and survey the major types of right-oriented GQs traditionally studied under GQT (including both monadic and iterated GQs). I also expand the scope of this theory to the analysis of left-oriented GQs (including left conservative GQs such as "only" and left-iterated GQs manifested as quantified statements with relative clauses). In Chapter 2, I introduce the major aspects of scalar reasoning to be studied in this thesis and summarize the major findings in the literature. After reviewing different notions of scales, I introduce other essential concepts and review the various theories and schools on the two main types of scalar reasoning, i.e. scalar entailments (SEs) and scalar implicatures (SIs). I then introduce four types of scalar lexical items studied under the Scalar Model Theory and Chinese grammar and discuss how their semantics / pragmatics are related to SEs and/or SIs. These include scalar operators (SOs), climax construction connectives (CCCs), subjective quantity operators (SQOs) and lexical items denoting extreme values. In the final part of this chapter, some outstanding problems in the studies on scalar reasoning are identified. In Chapter 3, I study four main types of quantifier inferences. They are monotonicity inferences, argument structure inferences, opposition inferences and (non-classical) syllogistic inferences. The major findings are summarized in tables and theorems. Special emphasis is put on devising general principles and methods that enable us to derive valid inferential patterns of iterated GQs from the inferential properties of their constituent monadic GQs. In Chapter 4, I apply the major findings worked out in the previous chapter to resolve the outstanding problems identified in Chapter 2. I first develop a basic formal framework that is based on the notions of generalized fractions and I-function. This basic framework can deal with the various aspects of scalar reasoning in a uniform way. I then enrich the basic framework by adding specific ingredients to deal with the phenomena of SEs and SIs. To deal with SEs, I add a relation connecting the I-function and SEs to the basic framework, so that the derivation of SEs is reduced to comparison between the I-function values of propositions. Moreover, by capitalizing on a parallelism between SEs and monotonicity inferences, I combine findings of the two types of inferences and discover new inferential patterns, such as Proportionality Calculus and scalar syllogisms. To deal with SIs, I add the ingredients of question under discussion (QUD) foci, answer exhaustification and opposition inferences to the basic framework, so that it can account for the various types of SIs and related phenomena introduced in Chapter 2 in a uniform way. I then use the framework to conduct a cross-linguistic study on the English and Chinese scalar lexical items introduced in Chapter 2. The I-function is used to formulate the conditions of use for these lexical items. The association of SEs and SIs with different types of scalar lexical items is also explored. Finally, Chapter 5 discusses the significance of the major findings of this thesis and possible extensions of the study.