On the Complexity and Properties of Preferential Propositional Dependence Logic
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.
Cite
@article{arxiv.2505.08522,
title = {On the Complexity and Properties of Preferential Propositional Dependence Logic},
author = {Kai Sauerwald and Arne Meier and Juha Kontinen},
journal= {arXiv preprint arXiv:2505.08522},
year = {2025}
}