Compilability and compact representations of revision of Horn knowledge bases

Abstract

Several methods have been proposed as an attempt to deal with dynamically-changing scenarios. From a computational point of view, different formalisms have different computational properties. In this paper we consider knowledge bases represented as sets of Horn clauses. The importance of this case is twofold: first, inference is polynomial, thus tractable; second, Horn clauses represent causal relations between facts, thus they are of great practical importance, although not all propositional knowledge bases can be represented in Horn form.The complexity of Horn revision is still high, and in some cases coincides with the complexity of the general (non-Horn) case. We analyze the complexity of belief revision from the point of view of the compilation ]: we study the possibility of reducing the complexity by allowing a (possibly expensive) preprocessing of part of the input of the problem.Extending the work of Cadoli, Donini, Liberatore, and Schaerf [1999], we consider the problem of compact representation of revision in the Horn case, that is, given a knowledge base T and an update P (both represented by Horn clauses) decide whether T * P , the result of the revision, can be represented with a propositional formula whose size is polynomial in the size of T and P . We give this representation for all formalisms for which it exists, and we show that the existence of a compact representation is related to the possibility of decreasing the complexity of a formalism via a preprocessing.

Belief revision within fragments of propositional logic

“…While the complexity of revision in the propositional case has been largely investigated [8,16,9,17,14,15] there are very few results on propositional sublanguages. As far as we know only the Horn fragment has been investigated.…”

“…The first mention of the Horn case for belief revision appears in [8], an analysis of belief revision complexity. In [14] a compact representation for revision in the Horn case is proposed. In [13] the study of belief revision in the Horn case provides a characterization of the existence of a complement of the Horn consequence which corresponds to a contraction operator.…”

The ghosts of forgotten things: A study on size after forgetting

“…Such properties are not limited to forgetting. They matter when minimizing a formula without forgetting [19,6]; they matter when minimizing the result of revising a formula [5,21,23] or circumscribing it [28]; they matter whenever a formula is produced, and minimizing it makes sense. Some clauses may be superirredundant out of the box.…”

Incremental Neural Network Training with an Increasing Input Dimension

“…Second, and perhaps more important, it demonstrates how such results can be obtained with the aid of the formal tools introduced in Peppas et al 2 More precisely, from situation calculus (Greiner & Elkan, 1991). 3 It should he noted that others have also worked on similar notions Wkecompactness and space efficiency-see for example (Cadoli, 2000;Greiner & Elkan, 1991;Liberatore, 2000)-but in most cases this work relates to broader issues in Knowledge Representation and is not specifically tailored to the frame problem.…”