On the Complexity and Properties of Preferential Propositional Dependence Logic

2025-05-13

AI Summary

This paper investigates the logical properties and computational complexity of KLM-style preferential reasoning in propositional dependence logic—based on team semantics and dependence atoms. Addressing whether preferential team reasoning satisfies cumulativity and the System P axioms, we provide the first intuitive and complete semantic characterization showing that it indeed validates System P; crucially, we demonstrate that this property fails in standard team logic without dependence atoms, thereby revealing the essential role of dependence atoms. We further construct nontrivial preferential models that precisely characterize the expressive power of preferential team reasoning with respect to both classical and dependence-logical entailment. Regarding complexity, we establish tight bounds: preferential team reasoning is PSPACE-complete under one natural representation and EXPTIME-complete under another, yielding novel complexity results for classical preferential reasoning as corollaries.

Technology Category

• Knowledge Representation and Reasoning: Preferences
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

This paper considers the complexity and properties of KLM-style preferential reasoning in the setting of propositional logic with team semantics and dependence atoms, also known as propositional dependence logic. Preferential team-based reasoning is shown to be cumulative, yet violates System~P. We give intuitive conditions that fully characterise those cases where preferential propositional dependence logic satisfies System~P. We show that these characterisations do, surprisingly, not carry over to preferential team-based propositional logic. Furthermore, we show how classical entailment and dependence logic entailment can be expressed in terms of non-trivial preferential models. Finally, we present the complexity of preferential team-based reasoning for two natural representations. This includes novel complexity results for classical (non-team-based) preferential reasoning.

Problem

• Analyzes complexity of preferential propositional dependence logic
• Characterizes conditions satisfying System P in dependence logic
• Compares classical and team-based preferential reasoning complexity

Innovation

• Preferential team-based reasoning is cumulative
• Conditions characterise System~P satisfaction
• Classical entailment expressed via preferential models