<p>In multi-agent epistemic logics, common knowledge has been a central consideration of study. A generic common knowledge (<i>G.C.K.</i>) system is one that yields iterated knowledge <i>I</i>(&phiv;): 'any agent knows that any agent knows that any agent knows. . . &phiv;' for any number of iterations. Generic common knowledge yields iterated knowledge <i> G.C.K.</i>(&phiv;) &rarr; <i>I</i>(&phiv;) but is not necessarily logically equivalent to it. This contrasts with the most prevalent formulation of common knowledge <i>C</i> as equivalent to iterated knowledge. A spectrum of systems may satisfy the <i>G.C.K.</i> condition, of which <i>C</i> is just one. It has been shown that in the usual epistemic scenarios, <i>G.C.K.</i> can replace conventional common knowledge and Artemov has noted that such standard sources of common knowledge as public announcements of atomic sentences generally yield <i>G.C.K. </i> rather than <i>C.</i> </p><p> In this dissertation we study mathematical properties of generic common knowledge and compare them to the traditional common knowledge notion. In particular, we contrast the modal <i>G.C.K.</i> logics of McCarthy (e.g. <tt>M4</tt>) and Artemov (e.g. [special characters omitted]) with <i>C</i>-systems (e.g. [special characters omitted]) and present a joint <i>C/G.C.K.</i> implicit knowledge logic [special characters omitted] as a conservative extension of both. We show that in standard epistemic scenarios in which common knowledge of certain premises is assumed, whose conclusion does not concern common knowledge (such as Muddy Children, Wise Men, Unfaithful Wives, etc.), a lighter <i>G.C.K.</i>can be used instead of the traditional, more complicated, common knowledge. We then present the first fully explicit <i>G.C.K.</i> system <tt>LP</tt><i>_n</i>(<tt>LP</tt>). This justification logic realizes the corresponding modal system [special characters omitted] so that <i>G.C.K.</i>, along with individual knowledge modalities, can always be made explicit.</p>

<p> In 1988, Mayer published a strong form of Vaught's Conjecture for o-minimal theories. She showed Vaught's Conjecture holds, and characterized the number of countable models of an o-minimal theory <i>T</i> if <i> T</i> has fewer than continuum many countable models. Friedman and Stanley have shown that several elementary classes are Borel complete. In this thesis we address the class of countable models of an o-minimal theory <i>T </i> when <i>T</i> has continuum many countable models. Our main result gives a model theoretic dichotomy describing the Borel complexity of isomorphism on the class of countable models of <i>T</i>. The first case is if <i>T</i> has no simple types, isomorphism is Borel on the class of countable models of <i>T</i>. In the second case, <i> T</i> has a simple type over a finite set <i>A</i>, and there is a finite set <i>B</i> containing <i>A</i> such that the class of countable models of the completion of <i>T </i>over <i> B</i> is Borel complete.</p>

<p> There are many different ways to talk about the world. Some ways of talking are more expressive than others&mdash;that is, they enable us to say more things about the world. But what exactly does this mean? When is one language able to express more about the world than another? In my dissertation, I systematically investigate different ways of answering this question and develop a formal theory of expressive power. In doing so, I show how these investigations help to clarify the role that expressive power plays within debates in metaphysics, logic, and the philosophy of language.</p><p> When we attempt to describe the world, we are trying to distinguish the way things are from all the many ways things could have been&mdash;in other words, we are trying to locate ourselves within a region of logical space. According to this picture, languages can be thought of as ways of carving logical space or, more formally, as maps from sentences to classes of models. For example, the language of first-order logic is just a mapping from first-order formulas to model-assignment pairs that satisfy those formulas. Almost all formal languages discussed in metaphysics and logic, as well as many of those discussed in natural language semantics, can be characterized in this way. </p><p> Using this picture of language, I analyze two different approaches to defining expressive power, each of which is motivated by different roles a language can play in a debate. One role a language can play is to divide and organize a shared conception of logical space. If two languages share the same conception of logical space (i.e., are defined over the same class of models), then one can compare the expressive power of these languages by comparing how finely they carve logical space. This is the approach commonly employed, for instance, in debates over tense and modality, such as the primitivism-reductionism debate.</p><p> But a second role languages can play in a debate is to advance a conception or theory of logical space itself. For example, consider the debate between perdurantism, which claims that objects persist through time by having temporal parts located throughout that time, and endurantism, which claims that objects persist through time by being wholly present at that time. A natural thought about this debate is that perdurantism and endurantism are simply alternative but equally good descriptions of the world rather than competing theories. Whenever the endurantist says, for instance, that an object is red at time <i> t</i>, the perdurantist can say that the object&rsquo;s temporal part at <i>t</i> is red. On this view, one should conceive of perdurantism and endurantism not as theories picking out disjoint regions of logical space, but as theories offering alternative conceptions of logical space: one in which persistence through time is analogous to location in space and one in which it is not. A similar distinction applies to other metaphysical debates, such as the mereological debate between universalism and nihilism.</p><p> If two theories propose incommensurable conceptions of logical space, we can still compare their expressive power utilizing the notion of a translation, which acts as a correlation between points in logical space that preserves the language&rsquo;s inferential connections. I build a formal theory of translation that explores different ways of making this notion precise. I then apply this theory to two metaphysical debates, viz., the debate over whether composite objects exist and the debate over how objects persist through time. This allows us to get a clearer picture of the sense in which these debates can be viewed as genuine.</p><p>

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 166-175). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 166-175). Also available on the Internet.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1967. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

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D. Tech. Electrical Engineering. / Proposes a vision-based solution for intention recognition of a person from the motions of the head and the hand This solution is intended to be applied in the context of wheelchair bound individuals whose intentions of interest are the wheelchairs direction and speed variation indicated by a rotation and a vertical motion respectively. Both head-based and hand-based solutions are proposed as an alternative to solutions using joysticks pneumatic switches, etc.