Recent research in both native (L1) and non-native (L2) knowledge of quantifier scope has led to a number of competing beliefs about the nature of learner knowledge. With regard to native knowledge, it has been noted in the literature that there is a discrepancy between L1 child and adult performance in quantifier interpretation. This observed mismatch has led to the formulation of two conflicting analyses of the L1 data. Philip (1991, 1992, and 1995) and others (Philip and Takahashi, 1991; Roeper, Strauss and Pearson, 2004, 2005; DelliCarpini, 2003) propose that quantification is a natural acquisition process constrained by Universal Grammar (UG) in which children progressively mature in their competence until they converge upon an adult grammar. Conversely, Crain (1995, 1996, and 1998) and others (Musolino, Crain and Thornton, 2000; Musolino and Lidz, 2006) maintain that children as young as five years old have a mature competence and that the failure to apply semantic principles is the result of the infelicitous nature of experimental task items. Essentially, the former account posits imperfect child L1 competence, while the latter asserts perfect competence. Similar research in the non-native (L2) knowledge of quantifier scope has been motivated by two essential questions: 1) Is adult L2 acquisition constrained by the same innate linguistic mechanisms as L1 acquisition; and 2) what is the role of L1 knowledge in adult L2 acquisition? (Marsden, 2004b: 9). In consideration of these questions, two main approaches have been devised as predictive models (following Epstein, Flynn and Martohardjono, 1996; Grüter, Lieberman and Gualmini, 2008, 2010). Under the Full Transfer hypothesis, the learner is predicted to approach an L2 with the same values, settings and preferences of the L1, whereas under the Full Access account, the L2 learner is informed by the Language Faculty directly without the intervening effects of the L1 (Grüter et al., 2008: 47). A third approach, Schwartz and Sprouse's (1996) model, unites both Full Access and Full Transfer to explain L2 acquisition. The present study explores L1 Mandarin knowledge of L2 English quantifier scope in order to address the issue of perfect vs. imperfect competence (as applied to SLA), as well as the matter of access to UG vs. L1 transfer. Incorporating insights from DelliCarpini (2003), I first assess the presence of symmetric and exhaustive responses, which are indicative of an immature grammar. Crucially, I use one group (n=11) of L2 English speakers (low intermediate and advanced) in order to test for a maturational discrepancy that would putatively differ according to proficiency. Secondly, I identify a potential poverty of the stimulus situation: L1 transfer cannot account for the L2 acquisition of English non-isomorphic scope licensing by native speakers of Mandarin Chinese due to the Isomorphic Principle (Aoun and Li, 1993). If demonstrated, the ability of L2 learners to converge upon this semantic principle (non-isomorphism) will serve as potential evidence for access to Universal Grammar in adult non-native learners.

We describe contributions to algorithmic proof techniques for deciding the satisfiability of boolean combinations of many-variable nonlinear polynomial equations and inequalities over the real and complex numbers. In the first half, we present an abstract theory of Grobner basis construction algorithms for algebraically closed fields of characteristic zero and use it to introduce and prove the correctness of Grobner basis methods tailored to the needs of modern satisfiability modulo theories (SMT) solvers. In the process, we use the technique of proof orders to derive a generalisation of S-polynomial superfluousness in terms of transfinite induction along an ordinal parameterised by a monomial order. We use this generalisation to prove the abstract (“strategy-independent”) admissibility of a number of superfluous S-polynomial criteria important for efficient basis construction. Finally, we consider local notions of proof minimality for weak Nullstellensatz proofs and give ideal-theoretic methods for computing complex “unsatisfiable cores” which contribute to efficient SMT solving in the context of nonlinear complex arithmetic. In the second half, we consider the problem of effectively combining a heterogeneous collection of decision techniques for fragments of the existential theory of real closed fields. We propose and investigate a number of novel combined decision methods and implement them in our proof tool RAHD (Real Algebra in High Dimensions). We build a hierarchy of increasingly powerful combined decision methods, culminating in a generalisation of partial cylindrical algebraic decomposition (CAD) which we call Abstract Partial CAD. This generalisation incorporates the use of arbitrary sound but possibly incomplete proof procedures for the existential theory of real closed fields as first-class functional parameters for “short-circuiting” expensive computations during the lifting phase of CAD. Identifying these proof procedure parameters formally with RAHD proof strategies, we implement the method in RAHD for the case of full-dimensional cell decompositions and investigate its efficacy with respect to the Brown-McCallum projection operator. We end with some wishes for the future.

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Wh-indefinites in Chinese have received great attention and discussion in the literature. This thesis investigates the status of Chinese wh-indefinites and their behaviors in the so-called donkey sentence. A typical example of wh-indefinite will be like the following: (4) Ta bu xiang zai shuo shenme le he not want again say what LE ¡¥He does not want to say anything again.¡¦ ¥L¤£·Q¦A»¡¤°»ò¤F¡C In this thesis, accounts of wh-indefinites as variables, polarity items and quantifiers from Huang (1982), Li (1992), Cheng (1991, 1994) and Lin (1996, 1998) are provided and this thesis discusses the problems each account presents. Countering Li¡¦s (1992) work, this work argue that wh-indefinite like zenmeyang ¡¦how¡¦ and weishenme ¡¥why¡¦ cannot be directly treated as variables since they feature variables only if they appear after an auxiliary (under which situation they will express purpose or method) in a donkey sentence according to Tsai (1999, 2000), see the following examples: (5) a. Akiu hui wei (le) shenme cizhi wo jiu hui wei (le) shenme cizhi¡@ Akiu will for LE what resign I then will for LE what resign ¡¥If Akiu will resign for the purpose x, I will then also resign for the purpose x.¡¦ ªüQ·|¬°¡]¤F¡^¤°»òÃ㾡A§Ú´N·|¬°¡]¤F¡^¤°»òÃ㾡C b. *Akiu wei (le) shenme hui cizhi wo jiu wei (le) shenme hui cizhi Akiu for LE what will resign I then will LE what will resign Intended ¡¥If Akiu will resign because of the reason x, I will then also resign because of the reason x. *ªüQ¬°¤F¤°»ò·|Ã㾡A§Ú´N¬°¤F¤°»ò·|Ã㾡C (Tsai¡¦s 2000, 15 glossed and translated by the author) Avoiding treating wh-indefinites as variables, we may treat them as quantifiers according to Huang¡¦s observation. But Huang¡¦s (1982) quantifier account of wh-indefinites is also rejected because I observe that wh-indefinites do not exhibit island sensitivity. Then we are led to another treatment: treating wh-indefinites as polarity items because they are sensitive to polarity environment. Aside from the sensitivity to polarity environment, Lin¡¦s (1996) work argues that wh-indefinites are licensed as polarity items if the sentence is subject to NEEC- non-entailment of existence condition. NEEC tells us that if (part of) a sentence does not have the existential import of object; wh-words can be licensed as wh-indefinites. This faces challenge because there are cases presupposing existential import yet the wh-indefinite is licensed. In chapter 3, two types of donkey sentences are identified in Cheng and Huang¡¦s (1996) work and are accounted with different approaches-Unselective Binding and E-type analysis. Though accepting their viewpoint generally, Lin (1996) makes a distinction between one-case and multi-case reading and opens the possibility of universal interpretation in ruguo-conditionals. Later I introduce Indirect binding approach to account both types of donkey sentences. Indirect Binding argues that some quantified expression plays the role as associating the indefinite with the anaphoric element in donkey sentences: (6) [Everyone who ti keeps a dogj]i like itj. The example here captures the very basic idea of Indirect Binding: the chunk of expression, which has the indefinite a dog in its scope, c-commands the pronoun it and hence relates it to the indefinite. I extend it to the analysis of Chinese donkey sentences and discover that although Indirect Binding does not target at a particular status, the condition that the indirect binder must c-command the indefinite seems to suggest that c-commanding is the way of licensing a wh-indefinite, which echoes Li¡¦s and Cheng¡¦s analyses. In Chapter 4, I introduce wh-indefinites in Japanese and Korean respectively and conclude that quantificational force comes from the environment but not from wh-indefinites themselves, countering Huang (1982). Finally, I suggest that licensing a wh-word as a wh-indefinite is through being c-commanded by the relevant operators. It is so because of Li¡¦s and Cheng¡¦s observation of wh-indefinites licensing and also of a condition in Indirect Binding that indirect binders must c-command the indefinite in order to have it as in its scope, as I have mentioned. This thesis then provides a viewpoint that perhaps, wh-indefinites can be treated uniformly as polarity items considering that Indirect Binding approach explains their behavior in donkey sentences. This thesis also opens the door for analyzing wh-indefinites in donkey sentences under Indirect Binding in other languages. Keywords¡G Wh-indefinite, polarity item, variable, quantifier, donkey phenomenon, Indirect Binding

The three papers which make up this dissertation form part of a larger project, which aims to solve the `access problem' for realism about mathematics by providing a clear and plausible example of what a satisfying explanation of human accuracy about objective mathematical facts could look like. They fit into this project as follows. / Philosophy

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>Magister Scientiae - MSc / We introduce the concept of an algebraically closed field with emphasis of the basic model-theoretic results concerning the theory of algebraically closed fields. One of these nice results about algebraically closed fields is the quantifier elimination property. We also show that the theory of algebraically closed field with a given characteristic is complete and model-complete. Finally, we introduce the beautiful Ax-Grothendieck theorem and an application to it.

We investigate the expressive power of different fragments of higher-order logics over finite relational structures (or equivalently, relational databases) with special emphasis in higher-order logics of order greater than or equal three. Our main results concern the study of the effect on the expressive power of higher-order logics, of simultaneously bounding the arity of the higher-order variables and the alternation of quantifiers.

Linguists and philosophers of language have shown increasing interest in the expressions that refer to quantifiers: determiners like 'every' and 'many', in addition to determiner phrases like 'some king' and 'no cat'. This thesis addresses several puzzles where the way we understand quantifier expressions depends on features that go beyond standard truth conditional semantic meaning. One puzzle concerns the fact that it is often natural to understand 'Every king is in the yard' as being true if (say) all of the kings at the party are in the yard, even though the standard truth conditions predict it to be true if and only if every king in the universe is in the yard. Another puzzle emerges from the observation that 'Every American king is in the yard' sounds odd relative to contexts where there are no American kings, even though the standard truth conditions predict it to be trivially true. These puzzles have been widely discussed within linguistics and philosophy of language, and have implications for topics as diverse as the distinction between semantics and pragmatics and the ontological commitments of ordinary individuals. Yet few attempts have been made to incorporate discussions from the linguistics literature into the philosophical literature. This thesis argues that attending to the linguistics literature helps to address these puzzles. In particular, my solutions to these puzzles rely on notions from work on information structure, an often overlooked area of linguistics. I will use these notions to develop a new theory of the pragmatics of ordinary discourse, in the process of resolving the puzzles. In the first two chapters, I provide accessible overviews of key notions from the literature on quantifier expressions and information structure. In the third chapter, I discuss the problem of contextual domain restriction. In the fourth chapter, I consider the problems posed by empty restrictors. In the final chapter, I tackle the issue of category mistakes.

This study investigates the problem of quantifier scope ambiguity in natural languages and the various ways with which it has been accounted for, some of which are problematic for monotonic theories of grammar like Combinatory Categorial Grammar (CCG) which strive for solutions that avoid non-monotonic functional application, and assume complete transparency between the syntax and the semantics interface of a language. Another purpose of this thesis is to explore these proposals on examples from Turkish and to try to account for the meaning differences that may be caused by word order and see how the observations from Turkish fit within the framework of CCG.