arXiv:2605.21113v1 Announce Type: cross 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.
This is a theoretical computer science paper published on arXiv, representing ongoing academic research in logic and AI.
While foundational, the direct commercial or strategic implications are far removed and do not directly impact current market or geopolitical structures.
This paper refines understanding of the computational complexity of specific logical systems, which may eventually inform future AI development, but does not alter current practice.
Increased understanding of the theoretical limits and capabilities of certain AI-relevant logical systems.
Potential for this theoretical work to inform or optimize algorithms in future, more advanced AI systems.
Very long-term, extremely indirect contribution to the foundational robustness of AI, supporting novel agentic behaviors or advanced reasoning capabilities.
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Read at arXiv cs.AI