  Motivated by a growing market that involves buying and selling data over the
web, we study pricing schemes that assign value to queries issued over a
database. Previous work studied pricing mechanisms that compute the price of a
query by extending a data seller's explicit prices on certain queries, or
investigated the properties that a pricing function should exhibit without
detailing a generic construction. In this work, we present a formal framework
for pricing queries over data that allows the construction of general families
of pricing functions, with the main goal of avoiding arbitrage. We consider two
types of pricing schemes: instance-independent schemes, where the price depends
only on the structure of the query, and answer-dependent schemes, where the
price also depends on the query output. Our main result is a complete
characterization of the structure of pricing functions in both settings, by
relating it to properties of a function over a lattice. We use our
characterization, together with information-theoretic methods, to construct a
variety of arbitrage-free pricing functions. Finally, we discuss various
tradeoffs in the design space and present techniques for efficient computation
of the proposed pricing functions.
