Datalog: Bag Semantics via Set Semantics

TL;DR

This paper presents a translation of Datalog with bag semantics into set-based Datalog$^ ext{pm}$, enabling reasoning and query processing using existing set-based engines, and extends this approach to handle duplicates directly.

Contribution

It introduces a novel translation method from bag semantics to set semantics in Datalog, facilitating practical reasoning and extending to handle duplicates within Datalog$^ ext{pm}$.

Findings

The translation enables reasoning on bag semantics using set semantics foundations.

It allows existing query engines to process Datalog with bag semantics effectively.

The approach has potential applications in Multiset Relational Algebra and SPARQL.

Abstract

Duplicates in data management are common and problematic. In this work, we present a translation of Datalog under bag semantics into a well-behaved extension of Datalog, the so-called {\em warded Datalog}$^\pm$, under set semantics. From a theoretical point of view, this allows us to reason on bag semantics by making use of the well-established theoretical foundations of set semantics. From a practical point of view, this allows us to handle the bag semantics of Datalog by powerful, existing query engines for the required extension of Datalog. This use of Datalog$^\pm$ is extended to give a set semantics to duplicates in Datalog$^\pm$ itself. We investigate the properties of the resulting Datalog$^\pm$ programs, the problem of deciding multiplicities, and expressibility of some bag operations. Moreover, the proposed translation has the potential for interesting applications such as to Multiset Relational Algebra and the semantic web query language SPARQL with bag semantics.