A syntactic and semantic treatment of Japanese floating quantifiers is provided from a perspective of unification based grammatical theories and model theoretic semantics. The inventory of floating quantifiers under consideration includes not only familiar cardinals but also other quantificational elements such as universals. Syntactically, floating quantifiers are taken to be adverbial endocentric modifiers for some V-projections. Scrambling phenomena involving multiple floating quantifiers will also be accounted for without employing movement rules of any sort. Floating quantifiers function as semantic (but not syntactic) determiners (seen in the Generalized Quantifier theory) which establish a proper relationship between two sets (corresponding to a common noun and a one-place predicate) one of which functions as a domain of quantification. In addition to presenting the specifics of the syntactic and semantic accounts for the phenomena in question, this thesis considers consequences of the proposed account and offers a new perspective on a universal theory of quantification. A typological classification of language is proposed which establishes the opposition between 'floating quantifier oriented' vs. 'determiner oriented' languages. From this perspective, a comparison between Japanese and English is carried out and some typological differences between the two are shown to follow from the envisaged opposition.

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本研究通过语言中的量词系统来探索语言相对论的假说。在诸如汉语普通话这样的量词语言中，名词通过名量词之间的搭配关系可以被分成不同的类。属于同一个量词类的名词所指通常在形状，有生性或者功能等方面有着共同的特征。这个研究关注的问题是，使用量词语言是否会影响一个人对于日常物体间相似度的判断。 / 相较于非量词语言母语者来说，量词语言母语者可能是因为两个物体属于同一个量词类而倾向于认为它们彼此更相似（量词类假说），也可能是因为两个物体在形状、有生性和大小这些特征上有共同点而认为它们彼此更相似（量词特征假说）。为了检验这两种可能性，这个研究中涉及到了两种量词语言普通话和粤语。这两种语言的量词系统在量词特征方面有很多共同点，但在量词对于名词的分类上却有不同。 / 前两个实验通过比较北京普通话母语者，香港粤语母语者和欧洲语言母语者来检验两个量词假说。结果发现，中国被试和欧美被试在物体相似判断任务中表现出了明显的整体差异，而中国被试内部，即普通话和粤语被试之间则没有明显差异，两者表现十分相似。中国被试的结果主要对量词特征假说提供了支持，而非量词类假说。此前研究中发现的量词效应也并不完全是由于名量词搭配这一语言关系引起的。此外，在第三个实验中，通过测试北京普通话母语者和有高级汉语水平的欧洲语言母语者，还验证了语言内部因素，即量词类之间的差异对于量词效应的产生也会有影响。 / 这个研究的结果表明使用和学习一种量词语言可以影响一个人对于物体间相似度的判断，这一发现为语言相对论提供了证据。 / This study examines the hypothesis of linguistic relativity through classifier systems. In a classifier language like Mandarin, nouns can be categorized through the collocation relationship between nouns and classifiers into different categories. The referents of nouns in the same classifier categories usually have some features in common, such as shape, animacy or function. This study is concerned with whether speaking a classifier language can affect one's similarity judgment on everyday objects. / It is likely that classifier language speakers tend to judge two objects that belong to the same classifier category as similar (category-based classifier hypothesis). Alternatively, classifier language speakers attend to certain features (e.g. shape, animacy, and size) between objects more than do non-classifier language speakers (feature-based classifier hypothesis). In order to distinguish these two possibilities, two classifier languages were included in the investigation - Mandarin and Cantonese, which have much in common in terms of the semantic features of classifiers, but differ in the classifier categorization of nouns. / The first two experiments tested the two classifier hypotheses with Beijing Mandarin speakers, Hong Kong Cantonese speakers, and European language speakers. There was an overall difference between Chinese speakers and European language speakers, but Mandarin and Cantonese speakers behaved quite similarly in terms of similarity judgment. Lack of difference between Mandarin and Cantonese speakers gives more support to feature-based classifier hypothesis than to category-based classifier hypothesis. It suggests that the classifier effect reported in previous studies is not merely contributed by the classifier-noun collocation. Besides, some other within-language factors in terms of the differences between classifier categories can also account for the absence of classifier category effect. They were supported by the results of the third experiment, with Beijing Mandarin speakers and European language speakers who were advanced Mandarin learners as subjects. / Findings of this study offer evidence for linguistic relativity, by showing that our similarity judgment on objects can be influenced by speaking or learning a classifier language. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Wang, Ruijing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 123-127). / Abstracts also in Chinese; appendix includes Chinese. / Abstract --- p.iii / Table of Contents --- p.vi / List of Tables and Figures --- p.vii / Chapter 1 --- Classifiers in Mandarin and Cantonese --- p.1 / Chapter 1.1 --- Classifier languages --- p.1 / Chapter 1.2 --- Syntax of classifiers in Mandarin and Cantonese --- p.1 / Chapter 1.3 --- Types of classifiers in Chinese --- p.5 / Chapter 1.4 --- Classifier category and overlaps between classifier categories --- p.11 / Chapter 1.5 --- Classifier features --- p.16 / Chapter 2 --- Empirical studies of linguistic relativity on classifier languages --- p.20 / Chapter 2.1 --- Linguistic relativity --- p.20 / Chapter 2.2 --- Classifier hypothesis and count-mass noun hypothesis --- p.21 / Chapter 2.2 --- Empirical studies of the classifier hypothesis --- p.26 / Chapter 2.3 --- Empirical studies of count-mass noun hypothesis --- p.43 / Chapter 2.4 --- Summary --- p.51 / Chapter 3 --- Studies --- p.52 / Chapter 3.1 --- Pre-study 1: Classifier Survey --- p.52 / Chapter 3.2 --- Experiment 1A: Similarity judgment task with pictorial stimuli --- p.59 / Chapter 3.3 --- Experiment 1B: Similarity judgment task with word stimuli --- p.67 / Chapter 3.4 --- Experiment 2: testing the gradient classifier model --- p.78 / Chapter 4 --- General discussion --- p.92 / Chapter 4.1 --- Classifier effect as shape effect --- p.92 / Chapter 4.2 --- Classifier categories and classifier languages --- p.94 / Chapter 4.3 --- Classifier effect as preferred strategy and habitual thought --- p.101 / Chapter 4.4 --- The function of classifiers and the classifier effect --- p.103 / Chapter 4.5 --- Bilinguals and second language leaners --- p.104 / Chapter 4.6 --- Future studies --- p.105 / Chapter 5 --- Conclusion --- p.107 / Appendix --- p.108 / References --- p.123

“Hey can you help me move? I warn you I have a lot of books, though.” When we interpret such sentences we might assume that our friend is implying that there will be some heavy lifting, because she own “a lot of books”. If you’re opposed to heavy lifting, you probably want to know how many books your friend wants you to help her move. While it is easy to determine the quantities picked out by numerals, discovering the meaning of quantifiers, such as “a lot”, is less clear. For example, in a survey people gave different quantities for “a few” and “a lot” depending on the context they were asked about, choosing to give quantities as high as 76 for “a few friends on Facebook” and as low as 4 for “a lot of houses”. I ask what role context plays in these interpretations, and propose two possible hypotheses: the Fixed Quantities Hypothesis, and the Relative Quantities Hypothesis. The Fixed Quantities Hypothesis assumes that these terms pick out an exact range of quantities (e.g., 3-5 for “a few”) and that the effect of context is due to people being pragmatically generous in their interpretations (Leech, 1983; Brown & Levinson, 1987; Lasersohn, 1999). The Relative Quantities Hypothesis instead argues that the ranges picked out by each of the terms is relative to the context, and therefore these terms might be similar to relative gradable adjectives (e.g., the meaning of the word “tall” is dependent on the reference set, e.g., what counts as “tall” is different for a mug versus a building; Kennedy, 2007; Syrett, Kennedy, & Lidz, 2010). I attempt to tease apart these two theories by looking at whether people find certain quantities implausible for some contexts leading them to think a speaker is being sloppy (Experiment 1), whether the context effect persists even under light-to-no pragmatic pressure (Experiment 2), and whether we find the effect of context even with minimal knowledge of novel contexts (Experiment 3). The results favour the Relative Quantities Hypothesis, and I discuss potential future work investigating the role of distributional knowledge on quantifier mappings.

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“Hey can you help me move? I warn you I have a lot of books, though.” When we interpret such sentences we might assume that our friend is implying that there will be some heavy lifting, because she own “a lot of books”. If you’re opposed to heavy lifting, you probably want to know how many books your friend wants you to help her move. While it is easy to determine the quantities picked out by numerals, discovering the meaning of quantifiers, such as “a lot”, is less clear. For example, in a survey people gave different quantities for “a few” and “a lot” depending on the context they were asked about, choosing to give quantities as high as 76 for “a few friends on Facebook” and as low as 4 for “a lot of houses”. I ask what role context plays in these interpretations, and propose two possible hypotheses: the Fixed Quantities Hypothesis, and the Relative Quantities Hypothesis. The Fixed Quantities Hypothesis assumes that these terms pick out an exact range of quantities (e.g., 3-5 for “a few”) and that the effect of context is due to people being pragmatically generous in their interpretations (Leech, 1983; Brown & Levinson, 1987; Lasersohn, 1999). The Relative Quantities Hypothesis instead argues that the ranges picked out by each of the terms is relative to the context, and therefore these terms might be similar to relative gradable adjectives (e.g., the meaning of the word “tall” is dependent on the reference set, e.g., what counts as “tall” is different for a mug versus a building; Kennedy, 2007; Syrett, Kennedy, & Lidz, 2010). I attempt to tease apart these two theories by looking at whether people find certain quantities implausible for some contexts leading them to think a speaker is being sloppy (Experiment 1), whether the context effect persists even under light-to-no pragmatic pressure (Experiment 2), and whether we find the effect of context even with minimal knowledge of novel contexts (Experiment 3). The results favour the Relative Quantities Hypothesis, and I discuss potential future work investigating the role of distributional knowledge on quantifier mappings.

<p> Propositional proof complexity is a field of theoretical computer science which concerns itself with the lengths of formal proofs in various propositional proof systems. Frege systems are an important class of propositional proof systems. Extended Frege augments them by allowing the introduction of new variables to abbreviate formulas. Perhaps the largest open question in propositional proof complexity is whether or not Extended Frege is significantly more powerful that Frege. Several proof systems, each introducing new rules or syntax to Frege, have been developed in an attempt to shed some light on this problem.</p> <p> We introduce one such system, which we call H, which allows for the quantification of transpositions of propositional variables. We show that H is sound and complete, and that H's transposition quantifiers efficiently represent any permutation.</p> <p> The most important contribution is showing that a fragment of this proof system, H*1, is equivalent in power to Extended Frege. This is a complicated and rather technical result, and is achieved by showing that H*1 can efficiently prove translations of the first-order logical theory ∀PLA, a logical theory well suited for reasoning about linear algebra and properties of graphs.</p> / Thesis / Master of Science (MSc)

SMT-based verification analyzes reachability for transition systems represented by SMT formulae. Depending on the theories and the kinds of systems considered, various approaches have been proposed. Together, they form the Verification Modulo Theory (VMT) framework. This thesis delves into SMT-based verification of parameterized systems, emphasizing the challenges and novel solutions in verifying systems with an unbounded number of components. In this thesis, we first introduce a general framework to model such systems. Then, we introduce two novel algorithms that leverage the strengths of SMT for the verification of parameterized systems, focusing on the automation and reduction of computational complexity inherent in such tasks. These algorithms are designed to improve upon existing verification methods by offering enhanced scalability and automation, making them particularly suited for the analysis of distributed systems, network protocols, and concurrent programming models where traditional approaches may fail. Moreover, we introduce an algorithm for compositional verification that advances the capability to modularly verify complex systems by decomposing the verification task into smaller, more manageable sub-tasks. Additionally, we discuss the potential and ongoing application of these algorithms in an industrial project focusing on the design of interlocking logic. This particular application demonstrates the practical utility of our algorithms in a real-world setting, highlighting their effectiveness in improving the safety and reliability of critical infras- tructure. The theoretical advancements proposed in this thesis are complemented by a rig- orous experimental evaluation, demonstrating the applicability and effectiveness of our methods across a range of verification scenarios. Our work is implemented within an ex- tended framework of the MathSAT SMT solver, facilitating its integration into existing verification workflows. Overall, this research contributes to the theoretical underpinnings of Verification Modulo Theories (VMT) and offers tools and methodologies for the verification community, enhancing the capability to verify complex parameterized systems with greater efficiency and reliability.

Thesis. 1978. Ph.D.--Massachusetts Institute of Technology. Dept. of Linguistics and Philosophy. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND HUMANITIES. / Bibliography: leaves 246-251. / Ph.D.