Like I said, Inferno is definitely the strangest of the Hellraiser movies so far, because it doesn't really feel like a part of the franchise's mythos directly. It has feelings of a movie like Seven, or just about any other movie about a grizzled city police detective who gets in too deep in the dark side of life and descends into madness. There are tie-ins to the universe of Hellraiser with the puzzle box, the Cenobites, and Pinhead, who sadly is only in the movie for a very short time close to the end. The tie-ins are loose but not exactly forced, because the movie is really only about Joseph, which is awesome and a great story. Pinhead, and Joseph's hellish experiences with the Cenobites, are used more as metaphors for the movie's underlying theme.
And what they were trying to say with this movie was actually very well thought and poignant. The child's fingers that are found at each crime scene, the strange child's room that Joseph keeps visiting in his dreams, the child's voice calling out to him for help - the audience slowly finds out that that was all Joseph. The final set up where Joseph is confronted with Pinhead (who was disguising himself as a psychiatrist - kinda weird, but I'll go with it) reveals that this is all about him being in his own personal hell, where he is slowly cutting away at his soul, because of his life choices and the people he has hurt. I like that. I especially like how at the end, he actually doesn't get a second chance to change things. It harkens back to Joseph's conversation with his partner Tony earlier in the movie about palindromes - the movie ends the same way it begins, with Joseph still in the hell of the life he has created for himself.
I guess I could go on longer and talk about the acting, the effects (which are also really good), the filming style (which completely sells the movie), and those freaky sexy Wire Twin Cenobites and the Half-Chatterer, but the story is really the highlight of Hellraiser: Inferno and is what makes the movie successful to me and one of my favorites of the franchise so far. This is stepping up the game for the rest you Hellraiser sequels, so you better follow through!