Dependence in Propositional Logic: Formula-Formula Dependence and Formula Forgetting -- Application to Belief Update and Conservative Extension
This work addresses efficiency issues in AI tasks like belief update and conservative extension for researchers in logic and knowledge representation, but it appears incremental as it builds on existing concepts of dependence.
The paper tackles the problem of efficiently handling tasks in artificial intelligence by introducing two new notions of dependence in propositional logic: formula-formula dependence and formula forgetting, and applies them to belief update and conservative extension, resulting in a new update operator and a reduction of conservative extension to formula forgetting.
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.