Axiomatisation of general concept inclusions from finite interpretations

Borchmann, Daniel; Distel, Felix; Kriegel, Francesco

doi:10.1080/11663081.2016.1168230

Cited by 13 publications

(25 citation statements)

References 29 publications

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“…For a given X ⊆ C I and a role depth d there may be multiple MMSCs (always at least one [8]) but they are logically equivalent. So we write 'the' MMSC of X with role depth d (in symbols mmsc (X, I, d)), meaning a representative of such class of concepts.…”

Section: Description Graphs Products and Unravellingsmentioning

confidence: 99%

“…Lemma 20. [8] Let I = (∆ I , • I ) be a finite EL ⊥ interpretation. For all X ⊆ ∆ I and k ∈ N, it holds that ∅ |= mmsc mmsc (X, I, k) I , I, k ≡ mmsc (X, I, k) .…”

Section: B Proofs For Sectionmentioning

confidence: 99%

“…However, it is far from being trivial to avoid the step of creating an EL ⊥ gf p base in their approach. A simplification of the mentioned work has been proposed by Borchmann, Distel, and Kriegel (2016) where they show how to mine EL ⊥ finite bases with a predefined and fixed role depth for concept expressions [8]. As a consequence, the base is sound and complete only w.r.t.…”

Section: Introductionmentioning

confidence: 99%

“…Our work brings together the best of the approaches by Distel (2011) and Borchmann, Distel, and Kriegel (2016): we directly compute a finite EL ⊥ base that captures the whole language (not only up to a certain role depth). Instead of fixing a priori a role depth for mined CIs, we adapt the role depth depending on the objects considered during the computation of CIs.…”

Section: Introductionmentioning

confidence: 99%

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Mining EL Bases with Adaptable Role Depth

Guimarães¹,

Ozaki²,

Persia³

et al. 2021

Preprint

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In Formal Concept Analysis, a base for a finite structure is a set of implications that characterizes all valid implications of the structure. This notion can be adapted to the context of Description Logic, where the base consists of a set of concept inclusions instead of implications. In this setting, concept expressions can be arbitrarily large. Thus, it is not clear whether a finite base exists and, if so, how large concept expressions may need to be. We first revisit results in the literature for mining EL ⊥ bases from finite interpretations. Those mainly focus on finding a finite base or on fixing the role depth but potentially losing some of the valid concept inclusions with higher role depth. We then present a new strategy for mining EL ⊥ bases which is adaptable in the sense that it can bound the role depth of concepts depending on the local structure of the interpretation. Our strategy guarantees to capture all EL ⊥ concept inclusions holding in the interpretation, not only the ones up to a fixed role depth.

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Section: Description Graphs Products and Unravellingsmentioning

confidence: 99%

“…Lemma 20. [8] Let I = (∆ I , • I ) be a finite EL ⊥ interpretation. For all X ⊆ ∆ I and k ∈ N, it holds that ∅ |= mmsc mmsc (X, I, k) I , I, k ≡ mmsc (X, I, k) .…”

Section: B Proofs For Sectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Mining EL Bases with Adaptable Role Depth

Guimarães¹,

Ozaki²,

Persia³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The advantage of this approach is that logic formula can be further processed in an automatic manner for more discovered knowledge. In [18], concepts of FCA are extracted and generalized into logic description. At a higher level, logical axioms are extracted by finite interpretations on concept lattice [18].…”

Section: B a Logical Generalization Of Formal Concept Analysismentioning

confidence: 99%

Viral Logical Concept Analysis for Malware Conceptual Hierarchy Generation

Binh¹

2017

IJMLC

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Abstract-Automatic classification of virus samples into a concept hierarchy has been attracting much attention from malware research community. This would help anti-virus experts to have an obvious and systematic view on the landscape of virus samples, whose numbers have been rapidly increasing recently. However, it is not a trivial work, since malwares usually come in binary forms whose actions are complicated and obfuscated. Therefore, the typical data mining approaches based on feature extraction are not easily applied. In this paper, we introduce an approach using Formal Concept Analysis (FCA) to generate a malware hierarchy. Since virus behaviours are often described effectively by temporal logic, we extend formal paradigm of FCA by using Logical Concept Analysis (LCA), where concepts are generalized by logic formulas. We also enhance the basic LCA to Viral Logical Concept Analysis (V-LCA), where abstraction techniques are used to abstract formal concepts representing virus samples. Our approach has been applied in a real dataset of virus and promising experiment results have been acquired. Index Terms-Computer virus, malicious software, malware detection, formal concept analysis, logical concept analysis, viral logical concept analysis, conceptual clustering.

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Acquisition of Terminological Knowledge in Probabilistic Description Logic

Kriegel

2018

Lecture Notes in Computer Science

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Axiomatisation of general concept inclusions from finite interpretations

Cited by 13 publications

References 29 publications

Mining EL Bases with Adaptable Role Depth

Mining EL Bases with Adaptable Role Depth

Viral Logical Concept Analysis for Malware Conceptual Hierarchy Generation

Acquisition of Terminological Knowledge in Probabilistic Description Logic

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