Over the past two years, a thriving market for licensing copyrighted material to train artificial intelligence systems has emerged. OpenAI was the first to strike deals with publications, like Axel Springer, News Corp. and the Associated Press. A few others in the field followed.

Such agreements weren’t in place when AI firms first started to face litigation accusing them of widespread infringement. Now, lawsuits are increasingly targeting the existence of this licensing market to argue that AI companies are illegally pilfering creators’ works.

Authors, in a proposed class action filed on Monday evening, accused Anthropic of illegally downloading and copying their books to power its AI chatbot Claude. The lawsuit alleges that the Amazon-backed company “usurped a licensing market for copyright owners.”

Without intervention from Congress, the legality of using copyrighted works in training datasets will be decided by the courts. The question will likely be answered in part on fair use,...