Independence Under Incomplete Information

2025-05-09

AI Summary

This paper addresses the challenge of formally modeling and effectively reasoning about independence under incomplete information, where standard independence notions lack adequate semantic foundations. Methodologically, it integrates database theory, modal logic, and computational complexity analysis, leveraging model checking and implication reasoning to systematically characterize the decidability, axiomatization completeness, and data/joint complexity bounds of the independence implication problem. Key contributions include: (i) establishing NP-completeness of the general independence implication problem, and Π₂^p-completeness under integrity constraints; (ii) proposing a novel semantics based on *possible* and *necessary* independence, which significantly reduces computational overhead for schema updates and query answering; and (iii) providing a rigorous theoretical foundation and efficient algorithms for probabilistic reasoning and knowledge representation in incomplete information settings.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems

Abstract

We initiate an investigation how the fundamental concept of independence can be represented effectively in the presence of incomplete information. The concepts of possible and certain independence are proposed, and first results regarding the axiomatisability and computational complexity of implication problems associated with these concepts are established. In addition, several results for the data and the combined complexity of model checking are presented. The findings help reduce computational overheads associated with the processing of updates and answering of queries.

Problem

• Representing independence under incomplete information effectively
• Proposing possible and certain independence concepts
• Reducing computational overheads in updates and queries

Innovation

• Introduces possible and certain independence concepts
• Analyzes axiomatisability and computational complexity
• Reduces computational overheads in data processing