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In this thesis I examine a variety of linguistic elements which involve ``alternative'' semantic values---a class arguably including focus, interrogatives, indefinites, and disjunctions---and the connections between these elements. This study focusses on the analysis of such elements in Sinhala, with comparison to Malayalam, Tlingit, and Japanese. The central part of the study concerns the proper syntactic and semantic analysis of Q[uestion]-particles (including Sinhala "da", Malayalam "-oo", Japanese "ka"), which, in many languages, appear not only in interrogatives, but also in the formation of indefinites, disjunctions, and relative clauses. This set of contexts is syntactically-heterogeneous, and so syntax does not offer an explanation for the appearance of Q-particles in this particular set of environments. I propose that these contexts can be united in terms of semantics, as all involving some element which denotes a set of ``alternatives''. Both wh-words and disjunctions can be analysed as creating Hamblin-type sets of ``alternatives''. Q-particles can be treated as uniformly denoting variables over choice functions which apply to the aforementioned Hamblin-type sets, thus ``restoring'' the derivation to normal Montagovian semantics. The treatment of Q-particles as uniformly denoting variables over choice functions provides an explanation for why these particles appear in just this set of contexts: they all include an element with Hamblin-type semantics. However, we also find variation in the use of Q-particles; including, in some languages, the appearance of multiple morphologically-distinct Q-particles in different syntactic contexts. Such variation can be handled largely by positing that Q-particles may vary in their formal syntactic feature specifications, determining which syntactic contexts they are licensed in. The unified analysis of Q-particles as denoting variables over choice functions also raises various questions about the proper analysis of interrogatives, indefinites, and disjunctions, including issues concerning the nature of the semantics of wh-words and the syntactic structure of disjunction. As well, I observe that indefinites involving Q-particles have a crosslinguistic tendency to be epistemic indefinites, i.e. indefinites which explicitly signal ignorance of details regarding who or what satisfies the existential claim. I provide an account of such indefinites which draws on the analysis of Q-particles as variables over choice functions. These pragmatic ``signals of ignorance'' (which I argue to be presuppositions) also have a further role to play in determining the distribution of Q-particles in disjunctions. The final section of this study investigates the historical development of focus constructions and Q-particles in Sinhala. This diachronic study allows us not only to observe the origin and development of such elements, but also serves to delimit the range of possible synchronic analyses, thus providing us with further insights into the formal syntactic and semantic properties of Q-particles. This study highlights both the importance of considering various components of the grammar (e.g. syntax, semantics, pragmatics, morphology) and the use of philology in developing plausible formal analyses of complex linguistic phenomena such as the crosslinguistic distribution of Q-particles.