It was the subject of quite some debate, see "Panel: Is J a Dialect of APL?" at http://www.jsoftware.com/papers/Vector_8_2_BarmanCamacho.pdf . Ken and Roger backed off this stance after witnessing the controversy.

"Ken Iverson - The dictionary of J contains an introductory comment that J is a dialect of APL, so in a sense the whole debate is Ken's fault! He is flattered to think that he has actually created a new language."