A Logical Approach to Data-Driven Classification

Osswald, Rainer; Petersen, Wiebke

doi:10.1007/978-3-540-39451-8_20

Cited by 6 publications

(9 citation statements)

References 8 publications

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“…The term AOC-poset was introduced in [29,27]. AOC-posets were also used in applications of FCA to non-monotonic reasoning and domain theory [19], and to produce classifications from linguistic data [26,29,27], because of their capability to structure knowledge. Specific parts of the AOC-poset -mainly attribute-conceptswere used in several works, including refactoring of a class hierarchy (e.g.…”

Section: Fca Notationsmentioning

confidence: 99%

“…However, the concept lattice may have an exponential size in the number of objects or attributes. A canonical sub-order of the lattice is the so-called AOC-poset for Attribute/Object Concept poset (the term was coined in [29,27]), which is of much smaller size. Thus, it can be recommended in some specific applications, as it contains all the relevant information for retrieving all formal concepts.…”

Section: Introductionmentioning

confidence: 99%

“…Depending on the background of the authors, several names were given for denoting the same structures, as Galois lattice and concept lattice, Galois sub-hierarchy and AOC-poset. Some other names were also used such as knowledge space in [25] for knowledge representation purposes, pruned concept hierarchy in [18] for class inheritance hierarchy restructuring, Galois sub-hierarchy in [11] again for class inheritance hierarchy restructuring and property sharing, and finally AOC-poset in [26,29,27] for building classifications from linguistic data and in [19] for applications of Formal Concept Analysis (FCA) to non-monotonic reasoning.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Hermes: a simple and efficient algorithm for building the AOC-poset of a binary relation

Berry

Gutierrez

Huchard

et al. 2014

Ann Math Artif Intell

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International audienceGiven a relation $\Rel\subseteq\Obj\times\Attr$ on a set $\Obj$ of objects and a set $\Attr $ of attributes, the AOC-poset (Attribute/Object Concept poset), is the partial order defined on the ``introducers'' of objects and attributes in the corresponding concept lattice.In this paper, we present \hermes, a simple and efficient algorithm for building an AOC-poset which runs in $O(min\{nm,\,n^\alpha\})$, where $n$ is the number of objects and attributes, $m$ is the size of the relation, and $n^\alpha$ is the time required to perform matrix multiplication (currently $\alpha=2.376$).Finally, we compare the execution time of \hermes~with the execution time of other published algorithms which compute the AOC-poset: \ares, \ceres~and \pluton. We characterize the cases where each of these algorithms is relevant to use

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Section: Fca Notationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Hermes: a simple and efficient algorithm for building the AOC-poset of a binary relation

Berry

Gutierrez

Huchard

et al. 2014

Ann Math Artif Intell

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“…Osswald and Petersen [24,25] study an approach to encoding knowledge in order structures which is inspired from linguistics. They obtain a framework which is more flexible than formal concept analysis, and appears to be compatible with our results in Section 5 and [7].…”

Section: Related Workmentioning

confidence: 99%

“…From this perspective, it should be investigated under which conditions a context satisfies the hypotheses of Theorem 3. It would also be important to relate this result to those of [21], where domain theory and formal concept analysis are being related by means of Chu space theory, and [24,25], where a general approach encompassing formal concept analysis is described for obtaining order structures carrying hierarchical knowledge.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

Default Reasoning over Domains and Concept Hierarchies

Hitzler¹

2004

KI 2004: Advances in Artificial Intelligence

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W.C. Rounds and G.-Q. Zhang have proposed to study a form of disjunctive logic programming generalized to algebraic domains [1]. This system allows reasoning with information which is hierarchically structured and forms a (suitable) domain. We extend this framework to include reasoning with default negation, giving rise to a new nonmonotonic reasoning framework on hierarchical knowledge which encompasses answer set programming with extended disjunctive logic programs. We also show that the hierarchically structured knowledge on which programming in this paradigm can be done, arises very naturally from formal concept analysis. Together, we obtain a default reasoning paradigm for conceptual knowledge which is in accordance with mainstream developments in nonmonotonic reasoning.

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Towards a Flexible and Scalable Data Stream Algorithm in FCA

Leutwyler,

Lezoche,

Torres

et al. 2023

Lecture Notes in Computer Science

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The amount of different environments where data can be exploited have increased partly because of the massive adoption of technologies such as microservices and distributed architectures. Accordingly, approaches to treat data are in constant improvement. An example of this is the Formal Concept Analysis framework that has seen an increase in the methods carried out to increment its capabilities in the mentioned environments. However, on top of the exponential nature of the output that the framework produces, the data stream processing environment still poses challenges regarding the flexibility in the usage of FCA and its extensions. Consequently, several approaches have been proposed to deal with them considering different constraints, such as receiving unsorted elements or unknown attributes. In this work, the notion of flexibly scalable for FCA distributed algorithms consuming data streams is defined. Additionally, the meaning of different scenarios of lattice merge in a particular data stream model is discussed. Finally, a pseudo-algorithm for merging lattices in the case of disjoint objects is presented. The presented work is a preliminary result and, in the future, it is expected to cover the other aspects of the problem with real data for validation.

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A Logical Approach to Data-Driven Classification

Cited by 6 publications

References 8 publications

Hermes: a simple and efficient algorithm for building the AOC-poset of a binary relation

Hermes: a simple and efficient algorithm for building the AOC-poset of a binary relation

Default Reasoning over Domains and Concept Hierarchies

Towards a Flexible and Scalable Data Stream Algorithm in FCA

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