Propositional Independence - Formula-Variable Independence and Forgetting

TL;DR

This paper explores syntactic and semantic notions of propositional independence and the process of forgetting in knowledge bases, analyzing their computational properties and implications for reasoning simplification.

Contribution

It introduces and compares two forms of propositional independence and examines the computational aspects of forgetting as a knowledge compilation technique.

Findings

Syntactic independence is computationally easier to check.

Semantic independence better captures intuitive relevance but is computationally harder.

Forgetting simplifies reasoning despite its computational complexity.

Abstract

Independence -- the study of what is relevant to a given problem of reasoning -- has received an increasing attention from the AI community. In this paper, we consider two basic forms of independence, namely, a syntactic one and a semantic one. We show features and drawbacks of them. In particular, while the syntactic form of independence is computationally easy to check, there are cases in which things that intuitively are not relevant are not recognized as such. We also consider the problem of forgetting, i.e., distilling from a knowledge base only the part that is relevant to the set of queries constructed from a subset of the alphabet. While such process is computationally hard, it allows for a simplification of subsequent reasoning, and can thus be viewed as a form of compilation: once the relevant part of a knowledge base has been extracted, all reasoning tasks to be performed can be simplified.