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arXiv · 2505.08522

On the Complexity and Properties of Preferential Propositional Dependence Logic

Kai Sauerwald·Arne Meier·Juha Kontinen
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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.

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Kai Sauerwald, Arne Meier, Juha Kontinen. 2025-05-13. On the Complexity and Properties of Preferential Propositional Dependence Logic. https://arxiv.org/abs/2505.08522

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