This PhD research project focuses on pioneering foundational theories in semantic communications, specifically by advancing the compositional learning and reasoning capabilities of AI agents within multi-agent environments. The goal is to enable AI-driven systems to selectively extract, interpret, and exchange semantically meaningful information in a goal-oriented and context-sensitive manner, moving beyond traditional data-oriented communications. Integrated Sensing and Communication (ISAC) will serve as a validation ground, introducing unique constraints related to resource optimization, multi-modal sensing, and environmental adaptability. However, the primary aim is to establish broadly applicable methodologies that enhance semantic information exchange and cooperation among AI agents. This involves rethinking the combination of modeling, numerical simulation, and experimental validation to effectively implement AI-driven semantic information exchange.