insight - Computational Complexity - # Consistent Query Answering for Existential Rules with Closed Predicates

Consistent Query Answering for Existential Rules with Closed Predicates

Q: How do the complexity results for CQA under the closed-world assumption compare to the open-world case, and what are the implications for practical applications

The complexity results for Consistent Query Answering (CQA) under the closed-world assumption differ from the open-world case in terms of the repair strategies employed. In the closed-world assumption, repairs are achieved through tuple deletions, whereas in the open-world assumption, repairs involve both tuple deletions and additions. This difference has implications for practical applications in data management and knowledge representation systems. Under the closed-world assumption, the problem of repair checking and consistent query answering can be more tractable for certain classes of existential rules. The identified classes of acyclic, linear, full, sticky, and guarded dependencies that are tractable and FO-rewritable provide insights into the computational complexity of CQA in databases with closed predicates. These results offer a more structured and efficient approach to handling inconsistencies in knowledge bases and databases, leading to potentially faster and more reliable query answering processes.

Q: Can the techniques developed in this paper be extended to handle other forms of inconsistency-tolerant reasoning, such as brave or cautious entailment

The techniques developed in this paper for handling inconsistency-tolerant reasoning under existential rules with closed predicates can potentially be extended to other forms of inconsistency management, such as brave or cautious entailment. Brave entailment involves considering all possible consequences of the available information, even if it leads to contradictions, while cautious entailment only considers consequences that are guaranteed to be true. By adapting the framework and algorithms developed for closed-world CQA to these different forms of entailment, it may be possible to provide consistent and meaningful answers to queries in scenarios where conflicting information exists. Extending the techniques to handle brave or cautious entailment would require modifications to the repair strategies and entailment semantics used in the existing framework. By incorporating the principles of brave and cautious reasoning into the repair and query answering processes, it could enhance the flexibility and applicability of the approach to a wider range of knowledge representation and reasoning tasks.

Q: What are the potential applications of the tractable and FO-rewritable classes of existential rules identified in this work, and how can they be leveraged in real-world knowledge representation and reasoning systems

The tractable and FO-rewritable classes of existential rules identified in this work have various potential applications in real-world knowledge representation and reasoning systems. Data Integration: These classes of existential rules can be leveraged in data integration systems to handle inconsistencies and conflicts that arise when merging data from multiple sources. By using the identified tractable classes, data integration processes can be streamlined and made more efficient. Knowledge Base Construction: In constructing knowledge bases for domains with incomplete or conflicting information, the identified classes of existential rules can help ensure consistency and accuracy in the knowledge representation. This is particularly useful in domains where maintaining data integrity is crucial. Query Answering Systems: The tractable classes of existential rules can be utilized in developing query answering systems that provide consistent and reliable answers to user queries. By leveraging the FO-rewritability property, these systems can efficiently process queries and handle inconsistencies in the underlying data. Overall, the identified classes of existential rules offer a structured and computationally efficient approach to handling inconsistencies in knowledge bases and databases, with applications spanning data integration, knowledge representation, and query answering systems.

Core Concepts

Consistent query answering (CQA) is an approach to inconsistency-tolerant reasoning in databases and knowledge bases. This paper studies CQA under the closed-world assumption, where the database predicates are assumed to have complete knowledge, and the only way to repair an inconsistency is through tuple deletions.

Abstract

The paper studies the problem of consistent query answering (CQA) in databases with data dependencies expressed by existential rules. Specifically, it focuses on the broad class of disjunctive embedded dependencies with inequalities (DEDs), which extend both tuple-generating dependencies and equality-generated dependencies.
The key points are:

The paper adopts a closed-world assumption, where the database predicates are assumed to have complete knowledge, and the only way to repair an inconsistency is through tuple deletions.
It provides a detailed analysis of the data complexity of repair checking and two inconsistency-tolerant query entailment semantics (AR and IAR) for different classes of existential rules, including acyclic, linear, full, sticky and guarded DEDs.
Many of the studied classes enjoy tractable complexity and first-order (FO) rewritability, which enables practical algorithms for consistent query answering based on FO rewriting methods.
The results complement the existing work on CQA under the open-world assumption, providing a comprehensive understanding of CQA under the closed-world semantics.

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Key Insights Distilled From

Consistent Query Answering for Existential Rules with Closed Predicates

by Lorenzo Marc... at arxiv.org 04-25-2024

https://arxiv.org/pdf/2401.05743.pdf

Consistent Query Answering for Existential Rules with Closed Predicates

Deeper Inquiries

How do the complexity results for CQA under the closed-world assumption compare to the open-world case, and what are the implications for practical applications

The complexity results for Consistent Query Answering (CQA) under the closed-world assumption differ from the open-world case in terms of the repair strategies employed. In the closed-world assumption, repairs are achieved through tuple deletions, whereas in the open-world assumption, repairs involve both tuple deletions and additions. This difference has implications for practical applications in data management and knowledge representation systems.
Under the closed-world assumption, the problem of repair checking and consistent query answering can be more tractable for certain classes of existential rules. The identified classes of acyclic, linear, full, sticky, and guarded dependencies that are tractable and FO-rewritable provide insights into the computational complexity of CQA in databases with closed predicates. These results offer a more structured and efficient approach to handling inconsistencies in knowledge bases and databases, leading to potentially faster and more reliable query answering processes.

Can the techniques developed in this paper be extended to handle other forms of inconsistency-tolerant reasoning, such as brave or cautious entailment

The techniques developed in this paper for handling inconsistency-tolerant reasoning under existential rules with closed predicates can potentially be extended to other forms of inconsistency management, such as brave or cautious entailment. Brave entailment involves considering all possible consequences of the available information, even if it leads to contradictions, while cautious entailment only considers consequences that are guaranteed to be true. By adapting the framework and algorithms developed for closed-world CQA to these different forms of entailment, it may be possible to provide consistent and meaningful answers to queries in scenarios where conflicting information exists.
Extending the techniques to handle brave or cautious entailment would require modifications to the repair strategies and entailment semantics used in the existing framework. By incorporating the principles of brave and cautious reasoning into the repair and query answering processes, it could enhance the flexibility and applicability of the approach to a wider range of knowledge representation and reasoning tasks.

What are the potential applications of the tractable and FO-rewritable classes of existential rules identified in this work, and how can they be leveraged in real-world knowledge representation and reasoning systems

The tractable and FO-rewritable classes of existential rules identified in this work have various potential applications in real-world knowledge representation and reasoning systems.

Data Integration: These classes of existential rules can be leveraged in data integration systems to handle inconsistencies and conflicts that arise when merging data from multiple sources. By using the identified tractable classes, data integration processes can be streamlined and made more efficient.

Knowledge Base Construction: In constructing knowledge bases for domains with incomplete or conflicting information, the identified classes of existential rules can help ensure consistency and accuracy in the knowledge representation. This is particularly useful in domains where maintaining data integrity is crucial.

Query Answering Systems: The tractable classes of existential rules can be utilized in developing query answering systems that provide consistent and reliable answers to user queries. By leveraging the FO-rewritability property, these systems can efficiently process queries and handle inconsistencies in the underlying data.

Overall, the identified classes of existential rules offer a structured and computationally efficient approach to handling inconsistencies in knowledge bases and databases, with applications spanning data integration, knowledge representation, and query answering systems.

Consistent Query Answering for Existential Rules with Closed Predicates