Browsing the TOS, it looks as though Wolfram is just trying to keep its options open — leaving sufficient wiggle room for some copyright-based claim int he future, while scaring the handful of users who might actually read this thing into providing attribution to Wolfram (and thus free advertising).

Sure, there may be copyrightable elements of the output of a computer program. The most obvious is something like MS Word — you type (creative) stuff in, and it puts words on a screen/page. That’s “output,” and it’s copyrightable subject matter. Of course, the creative elements are words typed in by the user; generally, the display elements the software uses aren’t the creative, copyrightable elements.
In many (if not most) cases, this is how Alpha seems to work — you put in a query, and it spits back some data relating to your query. The creative element of your search is largely what you put in, not what you got back.

Wolfram may be thinking (or to put it more precisely, the authors of Alpha’s TOS may be thinking) that its creative choices in deciding how to combine/compare the data inputs are copyrightable. I, like Mike, don’t think that’s likely. But there’s plenty of caselaw out there finding that the output of computer programs is copyrightable (a number of cases involving Blizzard come to mind). The courts in these cases may not have been sloppy, they may not have understood copyright or technology as well as they should have (and in some cases, that’s definitely true), but regardless of whether that’s true, there is authority out there that future courts might rely on to find Alpha’s output copyrightable.

By the way, another angle here is that Wolfram seems to be more or less asserting that a condition of use of the site is that users must treat the output as copyrightable, or rather, as something in which Wolfram retains attribution rights. Under that theory, a user who subsequently fails to give Alpha adequate attribution has violated the TOS, and Wolfram could then say that the user’s use of the site (i.e. downloading pages into a browser cache, or copying/cutting/pasting data) is some sort of infringement, as its a use not authorized by the license. (And yes – to answer the obvious, a purported contractual violation of this sort is by no means automatically a copyright violation, but courts have been split on this issue as well, so as the TOS says, it “may” constitute a violation of copyright law, even if it probably wouldn’t.)

Anyway, those are theories about what the heck WOlfram might be thinking. In general, they probably aren’t thinking that hard on this. Their lawyers are drafting the TOS as broadly as possible so as not to foreclose any legal claim, now known or later invented, they might want to make down the road.