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The Compactness of Belief Revision and Update Operators

Liberatore P., Schaerf M.

Fundamenta Informaticae

2004

Vol. 62, nr 3,4

377--393

A propositional knowledge base can be seen as a compact representation of a set of models. When a knowledge base T is updated with a formula P, the resulting set of models can be represented in two ways: either by a theory T' that is equivalent to T*P or by the pair ‹T,P›. The second representation can be super-polinomially more compact than the first. In this paper, we prove that the compactness of this representation depends on the specific semantics of *, , Winslett's semantics is more compact than Ginsberg's.

Sup-compact and inf-compact representations of W-operators

Barrera J., Hashimoto R.F.

Fundamenta Informaticae

2001

Vol. 45, nr 4

283-294

It is well known that any W-operator can be represented as the supremum (respectively, infimum) of sup-generating and (respectively, inf-generating) operators, that is, the families of sup-generating and inf-generating operators constitute the building blocks for representing W-operators. Here, we present two new families of building blocks to represent W-operators: compositions of sup-generating operators with dilations and compositions of inf-generating operators with erosions. The representations based on these new families of operators are called, respectively, sup-compact and inf-compact representations, since they may use less building blocks than the classical sup-generating and inf-generating representations. Considering the W-operators that are both anti-extensive and idempotent -in a strict sense-, we have also gotten a simplification of the sup-compact representation. We have also shown how the inf-compact representation can be simplified for any W-operator such that it is extensive and its dual operator is idempotent -in a strict sense-ź Furthermore, if the W-operators are openings (respectively, closings), we have shown that this simplified sup-compact (respectively, inf-compact) representation reduces to a minimal realization of the classical Matheron's representations for translation invariant openings (respectively, closings).