Dependence in Propositional Logic: Formula-Formula Dependence and Formula Forgetting -- Application to Belief Update and Conservative Extension
Abstract
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.
Cite
@article{arxiv.1806.11304,
title = {Dependence in Propositional Logic: Formula-Formula Dependence and Formula Forgetting -- Application to Belief Update and Conservative Extension},
author = {Liangda Fang and Hai Wan and Xianqiao Liu and Biqing Fang and Zhaorong Lai},
journal= {arXiv preprint arXiv:1806.11304},
year = {2019}
}
Comments
We find a mistake in this version and we need a period of time to fix it