Dependence in Propositional Logic: Formula-Formula Dependence and
  Formula Forgetting -- Application to Belief Update and Conservative Extension
  Dependence is an important concept for many tasks in artificial intelligence.
A task can be executed more efficiently by discarding something independent
from the task. In this paper, we propose two novel notions of dependence in
propositional logic: formula-formula dependence and formula forgetting. The
first is a relation between formulas capturing whether a formula depends on
another one, while the second is an operation that returns the strongest
consequence independent of a formula. We also apply these two notions in two
well-known issues: belief update and conservative extension. Firstly, we define
a new update operator based on formula-formula dependence. Furthermore, we
reduce conservative extension to formula forgetting.
