  Recursive queries have been traditionally studied in the framework of
datalog, a language that restricts recursion to monotone queries over sets,
which is guaranteed to converge in polynomial time in the size of the input.
But modern big data systems require recursive computations beyond the Boolean
space. In this paper we study the convergence of datalog when it is interpreted
over an arbitrary semiring. We consider an ordered semiring, define the
semantics of a datalog program as a least fixpoint in this semiring, and study
the number of steps required to reach that fixpoint, if ever. We identify
algebraic properties of the semiring that correspond to certain convergence
properties of datalog programs. Finally, we describe a class of ordered
semirings on which one can use the semi-na\"ive evaluation algorithm on any
datalog program.
