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The discipline usually called `probability theory' can be seen as the theory which describes and sets standard norms to the way we reason about plausibility. From this point of view, this `plausibility theory' is a province of logic, and the following informal proportion subsists: plausibility theory is to the common notion of `plausibility', as deductive logic is to the common notion of `truth'. Some studies in plausibility theory are here offered. An alternative view and mathematical formalism for the problem of induction (the prediction of uncertain events from similar, certain ones) is presented. It is also shown how from plausibility theory one can derive a mathematical framework, based on convex geometry, for the description of the predictive properties of physical theories. Within this framework, problems like state assignment - for any physical theory - find simple and clear algorithms, numerical examples of which are given for three-level quantum systems. Plausibility theory also gives insights on various fashionable theorems, like Bell’s theorem, and various fashionable `paradoxes', like Gibbs' paradox. / QC 20100816

In this dissertation, a normative prescriptive paradigm, namely a Bayesian theory of content-dependent argument strength, was employed in order to investigate argumentation, specifically the classic fallacy of the &ldquo / argument from ignorance&rdquo / or &ldquo / argumentum ad ignorantiam&rdquo / . The study was carried out in Turkish with Turkish participants. In the Bayesian framework, argument strength is determined by the interactions between three major factors: prior belief, polarity, and evidence reliability. In addition, topic effects are considered. Three experiments were conducted. The first experiment replicated Hahn et al.&rsquo / s (2005) study in Turkish to investigate whether similar results would be obtained in a different linguistic and cultural community. We found significant main effects of three of the manipulated factors in Oaksford and Hahn (2004) and Hahn et al. (2005): prior belief, reliability and topic. With respect to the Bayesian analysis, the overall fit between the data and the model was very good. The second experiment tested the hypothesis that argument acceptance would not vary across different intelligence levels. There was no significant main effect of prior belief, polarity, topic, and intelligence. We found a main effect of reliability only. However, further analyses on significant interactions showed that more intelligent subjects were less inclined to accept negative polarity items. Finally, the third experiment investigated the hypothesis that argument acceptance would vary depending on the presence of and the kind of evidentiality markers prevalent in Turkish, indicating the certainty with which events in the past have happened, marked with overt morpho-syntactic markers (&ndash / DI or &ndash / mIs). The experiment found a significant main effect of evidentiality as well as replicating the significant main effects of the two of the manipulated factors (prior belief and reliability) in Oaksford and Hahn (2004), Hahn et al. (2005) and in our first experiment. Furthermore, reliability and evidentiality interacted, indicating separate as well as combined effects of the two. With respect to the Bayesian analysis, the overall fit between the data and the model was lower than the one in the first experiment, but still acceptable. Overall, this study supported the normative Bayesian approach to studying argumentation in an interdisciplinary perspective, combining computation, psychology, linguistics, and philosophy.

<p>This thesis is concerned with scheduling the use of resources, or allocating resources, so as to meet future demands for the entities produced by the resources. We consider applications in mobile communications such as scheduling users' transmissions so that the amount of transmitted information is maximized, and scenarios in the manufacturing industry where the task is to distribute work among production units so as to minimize the number of missed orders.</p><p>The allocation decisions are complicated by a lack of information concerning the future demand and possibly also about the capacities of the available resources. We therefore resort to using probability theory and the maximum entropy principle as a means for making rational decisions under uncertainty.</p><p>By using probabilities interpreted as a reasonable degree of belief, we find optimum decision rules for the manufacturing problem, bidding under uncertainty in a certain type of auctions, scheduling users in communications with uncertain channel qualities and uncertain arrival rates, quantization of channel information, partitioning bandwidth between interfering and non-interfering areas in cellular networks, hand-overs and admission control. Moreover, a new method for making optimum approximate Bayesian inference is introduced.</p><p>We further discuss reasonable optimization criteria for the mentioned applications, and provide an introduction to the topic of probability theory as an extension to two-valued logic. It is argued that this view unifies a wide range of resource-allocation problems, and we discuss various directions for further research.</p>

This thesis is concerned with scheduling the use of resources, or allocating resources, so as to meet future demands for the entities produced by the resources. We consider applications in mobile communications such as scheduling users' transmissions so that the amount of transmitted information is maximized, and scenarios in the manufacturing industry where the task is to distribute work among production units so as to minimize the number of missed orders. The allocation decisions are complicated by a lack of information concerning the future demand and possibly also about the capacities of the available resources. We therefore resort to using probability theory and the maximum entropy principle as a means for making rational decisions under uncertainty. By using probabilities interpreted as a reasonable degree of belief, we find optimum decision rules for the manufacturing problem, bidding under uncertainty in a certain type of auctions, scheduling users in communications with uncertain channel qualities and uncertain arrival rates, quantization of channel information, partitioning bandwidth between interfering and non-interfering areas in cellular networks, hand-overs and admission control. Moreover, a new method for making optimum approximate Bayesian inference is introduced. We further discuss reasonable optimization criteria for the mentioned applications, and provide an introduction to the topic of probability theory as an extension to two-valued logic. It is argued that this view unifies a wide range of resource-allocation problems, and we discuss various directions for further research.