Measuring the blame of each formula for inconsistent prioritized knowledge bases

Mu, Kedian; Liu, Weiru; Jin, Zhi

doi:10.1093/jigpal/exr002

Cited by 28 publications

(37 citation statements)

References 19 publications

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“…Giving a vector value prioritized measure There are two types of prioritized knowledge bases described in [9], namely the Type-I and the Type-II prioritized knowledge base, which provide an intuitive ordering for formulae within a base. The approach of Type-I knowledge bases is to assign a numerical significance value to each formula.…”

Section: ∪θ ( )) Definition 44 (Max Siv) Letmentioning

confidence: 99%

“…, respectively, where 1 has the most important formulae, and the least. To begin defining the measure from [9] we must define the concept of Opposed formulae. This is the set of remaining formulae from a MIS resulting from the removal of a single formula from the MIS at each priority level.…”

Section: ∪θ ( )) Definition 44 (Max Siv) Letmentioning

confidence: 99%

“…Definition 4.8 (Opposed formulas [9]) Let be a minimal inconsistent prioritized knowledge base and a formula being attached with a priority level. Then the set of opposed formulae to w.r.t.…”

Section: ∪θ ( )) Definition 44 (Max Siv) Letmentioning

confidence: 99%

“…We continue defining the structure of the measure by introducing the measure from [9]. This, along with the Opposed formula, determines the value of a formula.…”

Section: Examplementioning

confidence: 99%

“…Accordingly inconsistency measures for flat knowledge bases need to be adapted for prioritized bases. The approach described in [9] demonstrates the significance of applying inconsistency measures to prioritized knowledge bases where the advantage of this approach is that the priority of a formula can be considered when measuring inconsistency.…”

Section: Introductionmentioning

confidence: 99%

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Measuring Inconsistency in Network Intrusion Rules

McAreavey

Liu

Miller

2011

2011 22nd International Workshop on Database and Expert Systems Applications

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Abstract-In this preliminary case study, we investigate how inconsistency in a network intrusion detection rule set can be measured. To achieve this, we first examine the structure of these rules which incorporate regular expression (Regex) pattern matching. We then identify primitive elements in these rules in order to translate the rules into their (equivalent) logical forms and to establish connections between them. Additional rules from background knowledge are also introduced to make the correlations among rules more explicit. Finally, we measure the degree of inconsistency in formulae of such a rule set (using the Scoring function, Shapley inconsistency values and Blame measure for prioritized knowledge) and compare the informativeness of these measures. We conclude that such measures are useful for the network intrusion domain assuming that incorporating domain knowledge for correlation of rules is feasible.

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Section: ∪θ ( )) Definition 44 (Max Siv) Letmentioning

confidence: 99%

Section: ∪θ ( )) Definition 44 (Max Siv) Letmentioning

confidence: 99%

Section: ∪θ ( )) Definition 44 (Max Siv) Letmentioning

confidence: 99%

“…We continue defining the structure of the measure by introducing the measure from [9]. This, along with the Opposed formula, determines the value of a formula.…”

Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Measuring Inconsistency in Network Intrusion Rules

McAreavey

Liu

Miller

2011

2011 22nd International Workshop on Database and Expert Systems Applications

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Counting Minimal Unsatisfiable Subsets

Bendík

Meel

2021

Computer Aided Verification

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Given an unsatisfiable Boolean formula F in CNF, an unsatisfiable subset of clauses U of F is called Minimal Unsatisfiable Subset (MUS) if every proper subset of U is satisfiable. Since MUSes serve as explanations for the unsatisfiability of F, MUSes find applications in a wide variety of domains. The availability of efficient SAT solvers has aided the development of scalable techniques for finding and enumerating MUSes in the past two decades. Building on the recent developments in the design of scalable model counting techniques for SAT, Bendík and Meel initiated the study of MUS counting techniques. They succeeded in designing the first approximate MUS counter, $$\mathsf {AMUSIC}$$ AMUSIC , that does not rely on exhaustive MUS enumeration. $$\mathsf {AMUSIC}$$ AMUSIC , however, suffers from two shortcomings: the lack of exact estimates and limited scalability due to its reliance on 3-QBF solvers.In this work, we address the two shortcomings of $$\mathsf {AMUSIC}$$ AMUSIC by designing the first exact MUS counter, $$\mathsf {CountMUST}$$ CountMUST , that does not rely on exhaustive enumeration. $$\mathsf {CountMUST}$$ CountMUST circumvents the need for 3-QBF solvers by reducing the problem of MUS counting to projected model counting. While projected model counting is #NP-hard, the past few years have witnessed the development of scalable projected model counters. An extensive empirical evaluation demonstrates that $$\mathsf {CountMUST}$$ CountMUST successfully returns MUS count for 1500 instances while $$\mathsf {AMUSIC}$$ AMUSIC and enumeration-based techniques could only handle up to 833 instances.

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