Belief Revision in Sentential Decision Diagrams

TL;DR

This paper introduces a new belief revision algorithm specifically designed for sentential decision diagrams (SDDs), a more compact and canonical representation of propositional knowledge, filling a gap in existing revision methods.

Contribution

The paper develops the first general belief revision algorithm for SDDs, extending Dalal revision to this class and providing a specialized procedure for DNFs.

Findings

Preliminary experiments show improved efficiency of direct revision in SDDs.

The algorithm maintains the desirable properties of belief revision within the SDD framework.

Abstract

Belief revision is the task of modifying a knowledge base when new information becomes available, while also respecting a number of desirable properties. Classical belief revision schemes have been already specialised to \emph{binary decision diagrams} (BDDs), the classical formalism to compactly represent propositional knowledge. These results also apply to \emph{ordered} BDDs (OBDDs), a special class of BDDs, designed to guarantee canonicity. Yet, those revisions cannot be applied to \emph{sentential decision diagrams} (SDDs), a typically more compact but still canonical class of Boolean circuits, which generalizes OBDDs, while not being a subclass of BDDs. Here we fill this gap by deriving a general revision algorithm for SDDs based on a syntactic characterisation of Dalal revision. A specialised procedure for DNFs is also presented. Preliminary experiments performed with randomly generated knowledge bases show the advantages of directly perform revision within SDD formalism.