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

arXiv: https://arxiv.org/abs/1806.11304 · HTML: https://mlsanity.com/paper/1806.11304/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2018.

## Built on by (most cited first, 2 of 2)

- [Superredundancy: A tool for Boolean formula minimization complexity analysis](https://mlsanity.com/paper/2205.00762/) (2022)
- [Abductive forgetting](https://mlsanity.com/paper/2209.12825/) (2022)

## Abstract (arXiv)

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.