# Epistemic Logic with Partial Dependency Operator

## TL;DR

This paper introduces a new partial dependency operator into epistemic logic, enhancing its expressivity to reason about partial dependencies in Kripke models, with formal properties and axiomatization.

## Contribution

It presents a novel partial dependency modality in epistemic logic, along with its formal properties, examples, bisimulation analysis, and a complete axiomatization.

## Key findings

- The logic can express partial dependency relationships.
- The logic has desirable properties like bisimulation invariance.
- A sound and complete axiomatization is provided for a sub-language.

## Abstract

In this paper, we introduce $\textit{partial}$ dependency modality $\mathcal{D}$ into epistemic logic so as to reason about $\textit{partial}$ dependency relationship in Kripke models. The resulted dependence epistemic logic possesses decent expressivity and beautiful properties. Several interesting examples are provided, which highlight this logic's practical usage. The logic's bisimulation is then discussed, and we give a sound and strongly complete axiomatization for a sub-language of the logic.