Abductive forgetting

TL;DR

Abductive forgetting involves removing variables from logical formulas while preserving explanations, with methods differing from standard consequence-preserving forgetting and involving complexity considerations and logic extensions.

Contribution

This paper introduces the concept of abductive forgetting, analyzes its properties, complexity, and conditions for expressibility, and proposes methods to ensure it can be represented.

Findings

Checking abductive forgetting is $ ext{Pi}_3^p$-complete.

Abductive forgetting may not be expressible as a propositional formula.

Switching to default logic or introducing new variables can guarantee expressibility.

Abstract

Abductive forgetting is removing variables from a logical formula while maintaining its abductive explanations. It is carried in two alternative ways depending on its intended application. Both differ from the usual forgetting, which maintains consequences rather than explanations. Differently from that, abductive forgetting from a propositional formula may not be expressed by any propositional formula. A necessary and sufficient condition tells when it is. Checking it is $\Pi^p_3$-complete. A way to guarantee expressibility of abductive forgetting is to switch from propositional to default logic. Another is to introduce new variables.