On the Complexity and Properties of Preferential Propositional Dependence Logic
Kai Sauerwald, Arne Meier, Juha Kontinen
TL;DR
The paper embeds KLM-style preferential reasoning inside the framework of propositional dependence logic under team semantics, defining ${\mathsf{PDL}}_{pref}$ and examining its inferential properties. It proves ${\mathsf{PDL}}_{pref}$ is cumulative but violates ${\mathsf{System\,P}}$, and identifies StarProperty and TriangleProperty as precise characterizations for when ${\mathsf{PDL}}_{pref}$ satisfies System ${\mathsf{P}}$, while showing these do not transfer to the team-based fragment ${\mathsf{TPL}}_{pref}$. It further introduces canonical preferential reconstructions for ${\mathsf{PDL}}$ and ${\mathsf{CPL}}$ that connect preferential entailment to classical entailment via flattening and sub/sup representations. The work provides a comprehensive complexity taxonomy for entailment in CPL_pref, PDL_pref, and TPL_pref across explicit and succinct representations, revealing nuanced computational boundaries and guiding future axiomatics and applications in knowledge representation and natural language semantics.
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.