Disjunctive datalog with existential quantifiers: Semantics, decidability, and complexity issues

@article{Alviano2012DisjunctiveDW,
  title={Disjunctive datalog with existential quantifiers: Semantics, decidability, and complexity issues},
  author={Mario Alviano and Wolfgang Faber and Nicola Leone and M. Manna},
  journal={Theory and Practice of Logic Programming},
  year={2012},
  volume={12},
  pages={701 - 718}
}
Abstract Datalog is one of the best-known rule-based languages, and extensions of it are used in a wide context of applications. An important Datalog extension is Disjunctive Datalog, which significantly increases the expressivity of the basic language. Disjunctive Datalog is useful in a wide range of applications, ranging from Databases (e.g., Data Integration) to Artificial Intelligence (e.g., diagnosis and planning under incomplete knowledge). However, in recent years an important… 
Query Answering over Disjunctive Datalog with Existential Quantifiers
TLDR
The paper discusses the impact of adding existential quantifiers in the head of positive disjunctive Datalog rules, and provides a notion of instantiation, which has been proven to be adequate for query answering purposes.
Fast Query Answering over Existential Rules
TLDR
The results in this article demonstrate that it is definitely possible to enable fast yet powerful query answering over existential rules that strictly generalize Datalog by ensuring decidability without any complexity overhead, and exploit the results to implement DLV∃, an effective system for queries answering over parsimonious existential rules.
On the Complexity of Ontological Reasoning under Disjunctive Existential Rules
TLDR
This paper enrichs Datalog even more by allowing not only existential quantification but also disjunction in rule heads, and investigates the complexity of reasoning under the obtained formalism.
The Impact of Disjunction on Query Answering Under Guarded-Based Existential Rules
TLDR
The main result states that conjunctive query answering under a fixed set of disjunctive IDs is 2EXPTIME-hard, and shows that frontier-guarded rules, combined with negative constraints, are strictly more expressive than DL-LiteboolH, one of the most expressive languages of the DL- Lite family.
Towards Efficient Reasoning Under Guarded-Based Disjunctive Existential Rules
TLDR
The central objective of the present paper is to understand whether the above query languages have a positive impact on the complexity of query answering under the main guarded-based classes of disjunctive existential rules.
Stable Model Semantics for Guarded Existential Rules and Description Logics: Decidability and Complexity
TLDR
This work investigates the decidability and complexity of database query answering under guarded existential rules with nonmonotonic negation according to the classical stable model semantics and considers extensions of the original formalism with negative constraints, keys, and the possibility of negated atoms in queries.
Acyclic Query Answering under Guarded Disjunctive Existential Rules and Consequences to DLs
TLDR
The main re-sult states that acyclic conjunctive query answering under a fixed set of guarded disjunctive existential rules is EXPTIME-hard, and shows that the results can be used as a generic tool for establishing results on (U)ACQ answering under several central DLs.
Expressive Completeness of Existential Rule Languages for Ontology-based Query Answering
TLDR
It is proved that disjunctive embedded dependencies exactly capture the class of recursively enumerable ontologies in Ontology-based Conjunctive Query Answering (OCQA).
Combining decidability paradigms for existential rules
TLDR
A powerful and flexible condition, called tameness, is proposed, which allows us to consolidate in an elegant and uniform way guardedness with stickiness.
Pay-as-you-go Ontology Query Answering Using a Datalog Reasoner
TLDR
Although the main goal is to efficiently answer queries over OWL 2 ontologies and data, the technical results are very general and the approach is applicable to first-order knowledge representation languages that can be captured by rules allowing for existential quantification and disjunction in the head.
...
...

References

SHOWING 1-10 OF 34 REFERENCES
Query Answering under Non-guarded Rules in Datalog+/-
TLDR
The complexity of query answering under Datalog+/- class of decidable languages is investigated, and in addition the novel class of sticky-join sets of TGDs is presented, which generalizes both sticky sets ofTGDs and so-called linear TGDs, an extension of inclusion dependencies.
New Expressive Languages for Ontological Query Answering
TLDR
This paper introduces a novel Datalog± language, namely sticky sets of TGDs, which allows for a wide class of joins in the body, while enjoying at the same time a low query-answering complexity, and properly generalizes both classical database constraints and most widespread tractable description logics.
Efficiently Computable Datalog∃ Programs
TLDR
The theoretical class of parsimonious Datalog∃ programs is defined, and it is shown that it allows of decidable and efficiently-computable reasoning, and the effectiveness of DLV∃ is confirmed, which outperforms all other systems in the benchmark domain.
Reducing SHIQ-Description Logic to Disjunctive Datalog Programs
TLDR
This paper presents a novel approach to checking consistency of ABoxes, instance checking and query answering, w.r.t. optimization techniques from deductive databases, and a resolution-based decision procedure for unary coding of numbers worst-case optimal.
A general datalog-based framework for tractable query answering over ontologies
TLDR
It is shown in particular that Datalog+/- generalizes the DL-Lite family of tractable description logics, which are the most common tractable ontology languages in the context of the Semantic Web and databases.
Advanced processing for ontological queries
TLDR
A more expressive formalism that takes joins into account, while still enjoying the same low query-answering complexity is introduced, and a highly expressive and effective ontological modeling language that unifies and generalizes both classical database constraints and important features of the most widespread tractable description logics is obtained.
Disjunctive datalog
TLDR
It is demonstrated that problems relevant in practice such as computing the optimal tour value in the Traveling Salesman Problem and eigenvector computations can be handled in disjunctive Datalog, but not Datalogs with negation (unless the Polynomial Hierarchy collapses).
Tractable Reasoning and Efficient Query Answering in Description Logics: The DL-Lite Family
TLDR
It is shown that, for the DLs of the DL-Lite family, the usual DL reasoning tasks are polynomial in the size of the TBox, and query answering is LogSpace in thesize of the ABox, which is the first result ofPolynomial-time data complexity for query answering over DL knowledge bases.
Ontological Query Answering with Existential Rules
TLDR
This paper focuses on the ontological query answering problem, which consists of querying data while taking ontological knowledge into account, and considers a logical framework based on existential rules, also called Tuple-Generating Dependencies or Datalog+/- rules.
Ontologies and Databases: The DL-Lite Approach
TLDR
This article addresses the problem of accessing relational data sources through an ontology, and presents a solution to the notorious impedance mismatch between the abstract objects in the ontology and the values appearing in data sources.
...
...