This book describes Probabilistic Logic Networks (PLN), a novel conceptual, mathematical and computational approach to uncertain inference. In order to carry out effective reasoning in real-world circumstances, AI software must robustly handle uncertainty. However, previous approaches to uncertain inference do not have the breadth of scope required to provide an integrated treatment of the disparate forms of cognitively critical uncertainty as they manifest themselves within the various forms of pragmatic inference. Going beyond prior probabilistic approaches to uncertain inference, PLN is able to encompass within uncertain logic such ideas as induction, abduction, analogy, fuzziness and speculation, and reasoning about time and causality. The book reviews the conceptual and mathematical foundations of PLN, giving the specific algebra involved in each type of inference encompassed within PLN. Inference control and the integration of inference with other cognitive faculties are also briefly discussed.