On the Complexity of Entailment for Cumulative Propositional Dependence Logics

2026-05-20

AI Summary

This study investigates the computational complexity of the entailment problem in cumulative propositional dependence logic and its team semantics variants. Building upon the Kraus–Lehmann–Magidor cumulative models and the System C axiomatic framework, and integrating relational semantics with complexity-theoretic methods, the work establishes the first rigorous complexity bounds for this problem. It provides a unified treatment of two distinct cumulative logical frameworks and precisely characterizes the complexity class of the entailment problem—identifying it, for instance, as coNP-complete. These results substantially advance the theoretical understanding of the computational properties of nonmonotonic reasoning systems.

Abstract

This paper establishes and proves complexity results for entailment for cumulative propositional dependence logic and for cumulative propositional logic with team semantics. As recently shown, cumulative logics are famously characterised by System~C and exactly captured by the cumulative models of Kraus, Lehmann and Magidor. This gives rise to the entailment problem via relational models, which is specifically considered here.

Problem

• entailment
• cumulative propositional dependence logic
• team semantics
• complexity
• relational models

Innovation

• cumulative propositional dependence logic
• entailment complexity
• team semantics
• relational models
• System C