Conservative Extensions for Existential Rules
Jean Christoph Jung, Carsten Lutz, Jerzy Marcinkowski
TL;DR
This paper investigates the decidability of conservative extensions in existential rules, revealing undecidability for certain classes and decidability for frontier-one TGDs, thus advancing understanding of rule extension properties.
Contribution
It provides a comprehensive analysis of the decidability of conservative extensions across different classes of existential rules, identifying cases of undecidability and decidability.
Findings
Undecidable for linear TGDs
Undecidable for guarded TGDs even when T1 is empty
Decidable for frontier-one TGDs
Abstract
We study the problem to decide, given sets T1,T2 of tuple-generating dependencies (TGDs), also called existential rules, whether T2 is a conservative extension of T1. We consider two natural notions of conservative extension, one pertaining to answers to conjunctive queries over databases and one to homomorphisms between chased databases. Our main results are that these problems are undecidable for linear TGDs, undecidable for guarded TGDs even when T1 is empty, and decidable for frontier-one TGDs.
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Taxonomy
TopicsLogic, Reasoning, and Knowledge · Advanced Database Systems and Queries · Distributed systems and fault tolerance