On the Complexity and Properties of Preferential Propositional Dependence Logic

TL;DR

This paper explores the complexity and properties of preferential reasoning in propositional dependence logic, revealing its cumulative nature, violations of System P, and providing complexity results for various models.

Contribution

It characterizes when preferential propositional dependence logic satisfies System P and analyzes the complexity of reasoning in team-based and classical models.

Findings

Preferential team-based reasoning is cumulative but violates System P.

Characterization of conditions for System P satisfaction in propositional dependence logic.

Complexity results for reasoning in team-based and classical preferential models.

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.