Logics for Propositional Determinacy and Independence

TL;DR

This paper introduces two new Kripke semantics-based logics, L_D and L_I, as alternatives to existing team semantics-based logics for propositional determinacy and independence, providing expressive analysis and axiomatizations.

Contribution

The paper presents L_D and L_I, new Kripke semantics-based logics for propositional determinacy and independence, with comparative analysis and complete axiomatizations.

Findings

L_D and L_I offer natural semantic alternatives to D and I.

The new logics resolve interpretational issues in propositional dependence and independence.

Sound and complete axiomatizations for L_D and L_I are established.

Abstract

This paper investigates formal logics for reasoning about determinacy and independence. Propositional Dependence Logic D and Propositional Independence Logic I are recently developed logical systems, based on team semantics, that provide a framework for such reasoning tasks. We introduce two new logics L_D and L_I, based on Kripke semantics, and propose them as alternatives for D and I, respectively. We analyze the relative expressive powers of these four logics and discuss the way these systems relate to natural language. We argue that L_D and L_I naturally resolve a range of interpretational problems that arise in D and I. We also obtain sound and complete axiomatizations for L_D and L_I.