Dyadic Existential Rules

TL;DR

This paper introduces Dyadic-$\

Contribution

It presents a new syntactic condition to systematically create decidable, expressive, and computationally efficient classes of existential rules that generalize Datalog and existing classes.

Findings

Dyadic-$\mathcal{C}$ classes are decidable and generalize Datalog.

They can leverage existing reasoners for the base class.

Computational complexity remains manageable, not exceeding the maximum of the base class and Datalog.

Abstract

Existential rules form an expressive Datalog-based language to specify ontological knowledge. The presence of existential quantification in rule-heads, however, makes the main reasoning tasks undecidable. To overcome this limitation, in the last two decades, a number of classes of existential rules guaranteeing the decidability of query answering have been proposed. Unfortunately, only some of these classes fully encompass Datalog and, often, this comes at the price of higher computational complexity. Moreover, expressive classes are typically unable to exploit tools developed for classes exhibiting lower expressiveness. To mitigate these shortcomings, this paper introduces a novel general syntactic condition that allows us to define, systematically and in a uniform way, from any decidable class $\mathcal{C}$ of existential rules, a new class called Dyadic-$\mathcal{C}$ enjoying the following properties: $(i)$ it is decidable; $(ii)$ it generalises Datalog; $(iii)$ it generalises $\mathcal{C}$; $(iv)$ it can effectively exploit any reasoner for query answering over $\mathcal{C}$; and $(v)$ its computational complexity does not exceed the highest between the one of $\mathcal{C}$ and the one of Datalog. Under consideration in Theory and Practice of Logic Programming (TPLP).