How is AI transforming the ways society decides what is true? Algorithms now go beyond detecting misinformation. They operate with agentic reasoning, identifying patterns, evaluating credibility, and shaping how truth is defined. Algorithmic Fact-Verification: Methods and Ethics explains how human judgment and machine intelligence intertwine in the creation of trust and credibility. It examines the social and moral consequences of giving AI an active role in verification, offering an accessible and thought-provoking account of how AI fact-checking is reshaping journalism, knowledge, and democracy in the digital age. Moving beyond the technicalities of misinformation detection, Shin analyzes how truth is produced, governed, and contested in the algorithmic age. Through a synthesis of communication theory, cognitive epistemology, and science and technology studies, we trace fact-checking's evolution from a reactive journalistic practice into an automated, infrastructural system endowed with epistemic agency. Emerging AI systems can autonomously identify misinformation patterns, generate hypotheses, and cross-validate claims across domains-turning verification into a self-reflective epistemic process. This shift marks the rise of agentic epistemology, where AI not only executes verification protocols but participates in reasoning, evaluation, and justification.Original frameworks such as Algorithmic Epistemology Theory and Cognitive Epistemic Modeling explain how algorithms construct, classify, and legitimize truth through probabilistic reasoning, datafication, and human-AI collaboration. The analysis unfolds across multiple levels: from cognitive biases that shape belief formation, to the infrastructural governance of algorithmic verification, to the ethical imperatives of transparency, fairness, and explainability. AI fact-checking does not simply detect falsehoods. It helps define the epistemic conditions under which truth becomes knowable. AI systems mediate credibility and knowledge while charting a path toward democratic and reflexive epistemic infrastructures in AI-mediated societies.