Enhancing the expressive power of the U-Datalog language

TL;DR

This paper enhances U-Datalog by introducing a stratified semantics to handle negation, thereby increasing its expressive power while analyzing the challenges in defining a compositional semantics.

Contribution

It proposes a stratified semantics for U-Datalog to explicitly handle negation, addressing its previous limitations in expressive power.

Findings

Stratified semantics enables explicit negation handling in U-Datalog.

Analysis of challenges in defining compositional semantics for the extended language.

Improved expressive power of U-Datalog with negation support.

Abstract

U-Datalog has been developed with the aim of providing a set-oriented logical update language, guaranteeing update parallelism in the context of a Datalog-like language. In U-Datalog, updates are expressed by introducing constraints (+p(X), to denote insertion, and [minus sign]p(X), to denote deletion) inside Datalog rules. A U-Datalog program can be interpreted as a CLP program. In this framework, a set of updates (constraints) is satisfiable if it does not represent an inconsistent theory, that is, it does not require the insertion and the deletion of the same fact. This approach resembles a very simple form of negation. However, on the other hand, U-Datalog does not provide any mechanism to explicitly deal with negative information, resulting in a language with limited expressive power. In this paper, we provide a semantics, based on stratification, handling the use of negated atoms in U-Datalog programs, and we show which problems arise in defining a compositional semantics.