Social science has developed an expansive design-based toolkit for applied causal inference, but the identifying assumptions that undergird standard approaches often fail in applied settings. However, when research questions cannot be precisely answered (not point-identified), it does not mean that nothing can be said about them; sharp bounds can be calculated through partial identification. The main challenge is that deriving these bounds can be complex. The dissertation is a collection of essays focusing on automating the process of drawing causal inference. Together, these papers provide methods for translating structural and functional causal assumptions, and observed data for any discrete causal inference problem into a form that can be analyzed computationally. After translating causal problems into this machine-readable form, it provides rigorous computational methods for obtaining maximally precise answers (point estimates or sharp bounds, depending on the amount of information available) and quantifying uncertainty. The first chapter describes and introduces a general framework for numerical partial identification solutions. The second chapter applies this method to the problem of identifying single-treatment effects in factorial experiments. The third chapter extends this framework to address problems related to transportability and external validity. The fourth chapter introduces a framework for closed-form partial solutions and illustrates its usefulness in the sensitivity analysis of relevant assumptions. The intellectual merit of the dissertation lies in the development of a framework and algorithms to automate key steps in causal reasoning as well as in the application of this framework to solve open problems such as sharp bounds for transportability, generalizing from factorial experiments, and flexible sensitivity analysis. In this sense, it does not only solve concrete causal inference problems but advance the research agenda of algorithmic-assisted causality.