Convergence of Datalog over (Pre-) Semirings

TL;DR

This paper explores how datalog, a recursive query language, converges over arbitrary semirings, extending traditional Boolean-based semantics to more complex algebraic structures relevant for big data systems.

Contribution

It introduces a framework for analyzing datalog convergence over ordered semirings and identifies algebraic properties that guarantee convergence and enable semi-na"ive evaluation.

Findings

Algebraic properties of semirings relate to datalog convergence.

Certain ordered semirings support semi-na"ive evaluation.

The study extends datalog semantics beyond Boolean logic.

Abstract

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.