Existential Rule Languages with Finite Chase: Complexity and Expressiveness
This work addresses the classification and complexity of rule languages for knowledge representation, but it is incremental as it builds on existing finite chase studies.
The authors tackled the problem of classifying existential rule languages with finite chase, a condition for decidability, and found that while all such languages are tractable for data complexity, their combined complexity can be arbitrarily high, and they proved that extensions of weakly acyclic languages have the same expressiveness but higher complexity languages are more succinct.
Finite chase, or alternatively chase termination, is an important condition to ensure the decidability of existential rule languages. In the past few years, a number of rule languages with finite chase have been studied. In this work, we propose a novel approach for classifying the rule languages with finite chase. Using this approach, a family of decidable rule languages, which extend the existing languages with the finite chase property, are naturally defined. We then study the complexity of these languages. Although all of them are tractable for data complexity, we show that their combined complexity can be arbitrarily high. Furthermore, we prove that all the rule languages with finite chase that extend the weakly acyclic language are of the same expressiveness as the weakly acyclic one, while rule languages with higher combined complexity are in general more succinct than those with lower combined complexity.