Learning to infer labels in an open world, i.e., in an environment where the target "labels" are unknown, is an important characteristic for achieving autonomy. Foundation models, pre-trained on enormous amounts of data, have shown remarkable generalization skills through prompting, particularly in zero-shot inference. However, their performance is restricted to the correctness of the target label's search space, i.e., candidate labels provided in the prompt. This target search space can be unknown or exceptionally large in an open world, severely restricting their performance. To tackle this challenging problem, we propose a two-step, neuro-symbolic framework called ALGO - Action Learning with Grounded Object recognition that uses symbolic knowledge stored in large-scale knowledge bases to infer activities in egocentric videos with limited supervision. First, we propose a neuro-symbolic prompting approach that uses object-centric vision-language models as a noisy oracle to ground objects in the video through evidence-based reasoning. Second, driven by prior commonsense knowledge, we discover plausible activities through an energy-based symbolic pattern theory framework and learn to ground knowledge-based action (verb) concepts in the video. Extensive experiments on four publicly available datasets (EPIC-Kitchens, GTEA Gaze, GTEA Gaze Plus, and Charades-Ego) demonstrate its performance on open-world activity inference. We also show that ALGO can be extended to zero-shot inference and demonstrate its competitive performance. Code and additional qualitative analysis are provided as part of the supplementary and will be publicly available after review.