Dependence in Propositional Logic: Formula-Formula Dependence and Formula Forgetting -- Application to Belief Update and Conservative Extension

TL;DR

This paper introduces two new notions of dependence in propositional logic—formula-formula dependence and formula forgetting—and applies them to belief update and conservative extension tasks, enhancing efficiency and understanding.

Contribution

It proposes novel dependence notions and demonstrates their application to belief update and conservative extension, providing new tools for AI reasoning tasks.

Findings

Defined a new update operator based on formula-formula dependence

Reduced conservative extension to formula forgetting

Enhanced reasoning efficiency in AI tasks

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.