The size of a revised knowledge base

Cadoli, Marco; Donini, Francesco M.; Liberatore, Paolo; Schaerf, Marco

doi:10.1016/s0004-3702(99)00074-0

Cited by 32 publications

(49 citation statements)

References 9 publications

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“…when T and P are allowed to be arbitrary formulas) Dalal's and Weber's operators have a compact representation w.r.t. query equivalence [Cadoli et al 1999]. In the Horn case, we prove that this holds also considering equivalence w.r.t.…”

Section: · 21mentioning

confidence: 65%

“…logical and model equivalence. Some results of Table 3 are also easy consequences of the results by Cadoli, Donini, Liberatore, and Schaerf [1999]: since Dalal's and Weber's revisions have a compact representation w.r.t. query equivalence in the general case, this representation also holds for the Horn case.…”

Section: Compact Representations Of Revisionmentioning

confidence: 81%

“…The result of WIDTIO can be trivially expressed as a formula which is at most as large as T ∧ P . The results proved by Cadoli, Donini, Liberatore, and Schaerf [1999] shows that, except for Dalal's and Weber's revision for the case of query equivalence, the result of revision can be superpolinomially larger than the knowledge base and the revising formula. In Table 4 we emphasize the difference between the general case and the Horn case.…”

Section: Compact Representations Of Revisionmentioning

confidence: 95%

“…For several important problems we can prove that they probably do not belong to ;P by proving their ;C-completeness for some C above P. For example, it can be easily shown that the problem Formula Inference (fi) defined as fi = { x, y | x and y are propositional formulae and x |= y } is ;coNP complete, with a ; reduction from * 3unsat. Nevertheless, for many natural problems the non-compilability proofs appeared in the literature [Kautz and Selman 1992;Cadoli et al 1997;Cadoli et al 1999;Gogic et al 1995;Liberatore 1995] cannot be rephrased as proofs of ;C-completeness.…”

Section: Definition 2 Given Two Problemsmentioning

confidence: 99%

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Compilability and compact representations of revision of Horn knowledge bases

Liberatore

2000

ACM Trans. Comput. Logic

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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.

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Section: · 21mentioning

confidence: 65%

Section: Compact Representations Of Revisionmentioning

confidence: 81%

Section: Compact Representations Of Revisionmentioning

confidence: 95%

Section: Definition 2 Given Two Problemsmentioning

confidence: 99%

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Compilability and compact representations of revision of Horn knowledge bases

Liberatore

2000

ACM Trans. Comput. Logic

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“…Knowledge compilation is defined in [8] as "methods of processing off-line a knowledge base in such a way that the output of such a pre-processing can be used to speed up on-line answering for a class of queries, where the pre-processing should take an finite amount of time". Within the area of knowledge compilation a distinction is made between exact methods (which are sound and complete) and approximate methods, which either reduce the complexity by expressing the knowledge or query in a simpler language or by leaving out some (complex) parts of the knowledge base.…”

Section: Related Researchmentioning

confidence: 99%

A Formal Approach to Aggregated Belief Formation

Heuvelink

Klein

Treur

2008

Cooperative Information Agents XII

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Abstract. This paper introduces a formal method to aggregate over basic beliefs, in order to deduce aggregated or complex beliefs as often used in applications. Complex beliefs can represent several things, such as a belief about a period in which other beliefs held or the minimal or maximal certainty with which a belief held. As such they contain richer information than the basic beliefs they are aggregated from and can be used to optimize an agent's search through its memory and its reasoning processes. The developed method can also aggregate over aggregated beliefs, hence nested aggregations are possible. An implementation in Prolog demonstrates its operationality.

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Preprocessing of Intractable Problems

Cadoli¹,

Donini

Liberatore³

et al. 2002

Information and Computation

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Some computationally hard problems-e.g., deduction in logical knowledge bases-are such that part of an instance is known well before the rest of it, and remains the same for several subsequent instances of the problem. In these cases, it is useful to preprocess off-line this known part so as to simplify the remaining on-line problem. In this paper we investigate such a technique in the context of intractable, i.e., NP-hard, problems. Recent results in the literature show that not all NP-hard problems behave in the same way: for some of them preprocessing yields polynomial-time on-line simplified problems (we call them compilable), while for other ones their compilability imply some consequences that are considered unlikely. Our primary goal is to provide a sound methodology that can be used to either prove or disprove that a problem is compilable. To this end, we define new models of computation, complexity classes, and reductions. We find complete problems for such classes, "completeness" meaning they are "the less likely to be compilable". We also investigate preprocessing that does not yield polynomial-time on-line algorithms, but generically "decreases" complexity. This leads us to define "hierarchies of compilability", that are the analog of the polynomial hierarchy. A detailed comparison of our framework to the idea of "parameterized tractability" shows the differences between the two approaches.

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The size of a revised knowledge base

Cited by 32 publications

References 9 publications

Compilability and compact representations of revision of Horn knowledge bases

Compilability and compact representations of revision of Horn knowledge bases

A Formal Approach to Aggregated Belief Formation

Preprocessing of Intractable Problems

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