Dialog Structure Induction (DSI) is the task of inferring the latent dialog structure (i.e., a set of dialog states and their temporal transitions) of a given goal-oriented dialog. It is a critical component for modern dialogue system design and discourse analysis. Existing DSI approaches are often purely data-driven, deploy models that infer latent states without access to domain knowledge, underperform when the training corpus is limited/noisy, or have difficulty when test dialogs exhibit distributional shifts from the training domain. This work explores a neural-symbolic approach as a potential solution to these problems. We introduce Neural Probabilistic Soft Logic Dialog Structure Induction (NEUPSL DSI), a principled approach that injects symbolic knowledge into the latent space of a generative neural model. Over three unsupervised dialog structure induction datasets the injection of symbolic knowledge using NEUPSL DSI provides a consistent boost in performance over the canonical baselines.