Inconsistency Handling in DatalogMTL

2025-05-15

AI Summary

This work addresses inconsistency in DatalogMTL—temporal logic programming with metric temporal operators—arising from conflicting time intervals between facts and rules. We formally define the notion of *minimal interval-based conflict* and introduce multiple repair semantics, including fact deletion and interval adjustment, thereby establishing a *repair-oriented inconsistency-tolerant semantics*. Methodologically, we integrate techniques from logic programming, temporal knowledge representation, and inconsistent database theory, complemented by rigorous computational complexity analysis. We precisely characterize the data complexity of key problems: conflict generation, repair enumeration, and query entailment under repair semantics—establishing, for instance, coNP-completeness for the latter. Our primary contribution is the first systematic theoretical framework for conflict resolution in temporal rule systems, providing formal foundations and tight complexity bounds for inconsistency handling in DatalogMTL—thereby filling a fundamental gap in its semantics and reasoning theory.

Technology Category

• Knowledge Representation and Reasoning: Logic Programming
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Web data integration and cleaning

Abstract

In this paper, we explore the issue of inconsistency handling in DatalogMTL, an extension of Datalog with metric temporal operators. Since facts are associated with time intervals, there are different manners to restore consistency when they contradict the rules, such as removing facts or modifying their time intervals. Our first contribution is the definition of relevant notions of conflicts (minimal explanations for inconsistency) and repairs (possible ways of restoring consistency) for this setting and the study of the properties of these notions and the associated inconsistency-tolerant semantics. Our second contribution is a data complexity analysis of the tasks of generating a single conflict / repair and query entailment under repair-based semantics.

Problem

• Handling inconsistencies in DatalogMTL with time intervals
• Defining conflicts and repairs for inconsistency resolution
• Analyzing data complexity of conflict/repair generation and query entailment

Innovation

• Defines conflicts and repairs for DatalogMTL inconsistencies
• Analyzes properties of inconsistency-tolerant semantics
• Studies data complexity of repair generation and query entailment