This study aims to investigate the dynamics of cognitive trust among patients in healthcare settings, with a focus on three distinct Artificial Intelligence (AI) representations: robotic AI (physical robots), virtual AI (virtual agents or bots), and embedded AI (technology integrated within devices or software, invisible to the user). The rapid integration of AI into healthcare highlights the urgent need to understand how patients perceive and trust these technologies. Addressing this need, our research evaluates the effects of key variables—tangibility, transparency, reliability, and task nature—on cognitive trust in each AI form. By analyzing responses from healthcare recipients, the study aims to uncover how these variables influence patients' cognitive trust level in AI-assisted healthcare services. The findings are expected to contribute valuable insights for the ethical design, implementation, and policy-making regarding AI in healthcare, ensuring these technologies are deployed in effective and trust-enhancing ways.