Probabilistic Analysis of Copyright Disputes and Generative AI Safety

This paper presents a probabilistic approach to analyzing copyright infringement disputes. Evidentiary principles shaped by case law are formalized in probabilistic terms, and the ``inverse ratio rule'' -- a controversial legal doctrine adopted by some courts -- is examined. Although this rule has faced significant criticism, a formal proof demonstrates its validity, provided it is properly defined. The probabilistic approach is further employed to study the copyright safety of generative AI. Specifically, the Near Access-Free (NAF) condition, previously proposed as a strategy for mitigating the heightened copyright infringement risks of generative AI, is evaluated. The analysis reveals limitations in its justifiability and efficacy.