The semijoin algebra and the guarded fragment

TL;DR

This paper explores the semijoin algebra, a variant of relational algebra, and its connections to the guarded fragment of first-order logic, including a game-based method to analyze its expressive power.

Contribution

It establishes links between the semijoin algebra and the guarded fragment, and introduces an Ehrenfeucht-Fraisse game to characterize its expressive capabilities.

Findings

The semijoin algebra is related to the guarded fragment of first-order logic.

The Ehrenfeucht-Fraisse game characterizes the expressive power of the semijoin algebra.

The game provides a method to show non-expressibility of certain queries.

Abstract

The semijoin algebra is the variant of the relational algebra obtained by replacing the join operator by the semijoin operator. We discuss some interesting connections between the semijoin algebra and the guarded fragment of first-order logic. We also provide an Ehrenfeucht-Fraisse game, characterizing the discerning power of the semijoin algebra. This game gives a method for showing that certain queries are not expressible in the semijoin algebra.