For a given domain D, we define that [D.sup.0] is a singleton set {(}}, so that {f, t} = P([D.sup.0]), where P is the

powerset operator.

The authors explain that "it seems best to say that a conditional is just any operator" (of any arity) over the

powerset of all models for a given language--thus including for example negation and conjunction which, however, are left aside from the discussion because "we know them well"!

(i) If X is a set and P(X) the

powerset of X, then (X; P(X)) is the discrete texture on X.

(1) If X is a set and P(X) the

powerset of X, then (X, P(X)) is the discrete texture on X.

Vendors offering NLP systems include Oracle, which bought the natural language provider InQuira in mid-2011, Microsoft via its acquisition of

Powerset and its licensing of the Cognition Technologies, Inc.

Set-theoretically, this can be expressed by z being a proper subset of the

powerset of X.

Cardo Systems, Inc., Pittsburgh, a market leader in wireless Bluetooth communications for helmet headsets, has announced the availability of its new wireless scala rider G4

PowerSet with corded rather than boom microphones and intercom system specifically designed for snowmobile riders.

A partition matrix on X is an upper triangular matrix over the

powerset of X satisfying the following properties:

For a long time Google didn't need to do much to remain the leader in internet search, focusing primarily on the "access" part of its self-proclaimed mission "to organize the world's information and make it universally accessible and useful." But runner-up Microsoft went out and bought Medstory in 2007 and then

Powerset in 2008.

Barney Pell, whose company

Powerset was also working on a conversational-search interface before it was acquired by Microsoft, dismissed the notion that a computerized entity could effectively fill the role of text, but he does acknowledge that breakthroughs of all sorts are possible.

When Microsoft's new search engine Bing was released in June, with technologies gained from the FAST and

Powerset acquisitions, outgunning Yahoo seach capabilities, Bartz knew that that something had to be dramatic.

Oh, and of course you overhaul the underlying technology, add in your recently acquired

Powerset technology, mix this with social search, wrap it up in stunning imagery and offer a new API.