The visualization of information is an astonishing cultural technique. It is employed in several scientific disciplines dealing with human reasoning, decision-making, and logical as well as statistical inference. Thus, visualization can be regarded as one of the most versatile forms of representation, and certainly one of the most ubiquitous ones. With the growing availabil- ity of digital computation power, visualization also became an interface between humans and machines, such as in visual analytics systems. Despite a long history of research from diverse angles and its wide application in practice, a unified broad theoretic foundation of why and how visualization facilitates human decision-making is missing. In this thesis, we contribute to the theoretic foundation of visualization, and apply some of our concepts to concrete examples. First, we construct a network of arguments that connects a wide range of theoretic arguments on why visualization works. Beyond collecting more than one hundred arguments, the network explicates dependencies between these arguments, as well as needs for trade-offs between opposing arguments. With the network, we identify the hypothetical compromise between the specificity and the flexibility of visualizations. We conduct the first experiment on the uninstructed transfer between two probabilistic inference tasks to investigate this expected trade-off empirically. Our experiment provides results that are only partially in line with our expectations. Furthermore, we introduce a representational framework that disentangles the visualization processes as experienced by designers and viewers. In particular, we describe how viewers benefit from an intricate division of labor with designers. Optimally, designers provide transparent visualizations that fit the tasks at hand. In a second experiment, we detail particular predictions of our representational framework on the tailoring of visualizations to Bayesian inference tasks, which are practically relevant in medical diagnosis and the evaluation of binary classification models. We find evidence that tailored visual representations can boost performance. However, additional experiments need to be undertaken in order to come up with a conclusive understanding of how representations alter inference processes. Methodologically, we high- light the importance of choosing appropriate performance measures for evaluating participants’ performance in tasks that promote highly structured error patterns. The commonly used mean absolute error measure can mislead in such scenarios, especially when comparing performance across tasks. Crucially, our representational framework extends beyond the presentation of priorily known answers to closed tasks, such as the positive predictive value in the case of Bayesian inference tasks. When dealing with open-ended inference and decision-making tasks, there are no such well-defined solutions. Instead, tasks are typically ill-posed and potential solutions are notoriously uncertain. As a result, viewers increasingly become designers by following unforeseen reasoning paths and by navigating through interactive visualizations and visual analytics systems. We present a conceptual workflow for joint model development as a theoretic basis of future visual analytics systems and demonstrate its feasibility in the context of interactive regression analysis. Throughout the modeling process, human reasoning is crucial, for example, in the evaluation and comparison of candidate models along with multiple objectives. We stress that reducing human involvement by the premature quantification and resolution of expected trade-offs risks limiting real-world performance and conflicts with the data-driven stance of machine learning. Applying our concepts to other contexts involving more open-ended tasks constitutes a major avenue for future research on visualization and visual analytics. Our network of arguments and our representational framework provides a broad foundation for empirical investigations of visualization. In the long run, decision-makers may be able to reason more effectively by utilizing visualizations build on the joint expertise of interdisciplinary research that we facilitated by exploring its theoretic foundation.