Belief Revision in Sentential Decision Diagrams

Lilith Mattei; Alessandro Facchini; Alessandro Antonucci

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arXiv · 2201.08112

Belief Revision in Sentential Decision Diagrams

Lilith Mattei·Alessandro Facchini·Alessandro Antonucci

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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.

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Lilith Mattei, Alessandro Facchini, Alessandro Antonucci. 2022-01-20. Belief Revision in Sentential Decision Diagrams. https://arxiv.org/abs/2201.08112

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