I like this logo. I think it's madness to launch a sixth and seventh ongoing monthly starring Batman (of which this title would be one), and I think it's confidence-bordering-on-madness to use "The Dark Knight" in it's title, constantly begging readers to subconsciously compare its contents against Frank Miller and company's The Dark Knight Returns and the last Batman movie, and if I were writer/artist David Finch, I'd rather have a title that lowered rather than raised expectations (Batman: Not That Bad maybe, or Batman: The Capable Crusader, perhaps).
But I think whoever designed the logo for the series did a rather swell job of it. I'm not sure how it will age—it doesn't seem to be a necessarily timeless design, and I may think better of what's going on with the N and the I in the future—but when I first saw it, I thought "Neat" and "Cool," and it was actually the first time I had positive thoughts about the series (I don't care for Finch's artwork, and the work I've seen most recently, his cover work for DC on titles like Brightest Day and Action Comics, has been pretty awful).
I like this one too. It's from the wraparound cover for Justice League of America #50. It's super-simple, just the JLA logo altered so that the name of the team of their evil opposites is in the shield instead of their name. Familiar things that looks only slightly different than usual can often be very appealing though, like an Elseworlds version of a Superman costume, or Cap'n Crunch's "crunch berries" going red and green during the Christmas holiday season. I'd probably buy a comic book with that logo. I probably wouldn't understand the book, but I'd probably buy it.
I don't like this logo. I'm not entirely sure why...it's the B and the two A's I don't care for. And, to a lesser extent, the W. The font and the shapes seem appropriate for the character and the setting, but...I don't know. Something about it just doesn't grab me.
I don't like this logo either. It looks very corporate, and like something that would be found on an expensive, mass-produced product, which makes it somewhat appropriate for the Batman Incorporated concept (as I understand it, anyway). But appropriate or not, it's still pretty ugly...Batman's got a pretty boss symbol, no matter how you tweak the shape and the edges, but breaking the bat-symbol in half, and the thin, light-colored line on a bigger-than-usual oval make for a very, very un-Batman-like bat-symbol.
Looks a little better in red. Maybe it will grow on me.