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The Chu construction and generalized formal concept analysis
2017
International Journal of General Systems
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The goal of this paper is to show a connection between FCA generalisations and the Chu construction on the category ChuCors, the category of formal contexts and Chu correspondences. ...
Finally, the second order generalisation of FCA is represented by a category built up in terms of the Chu construction. ...
As a first application, we have sketched the representation of second order formal concept analysis [14] in terms of the Chu construction on the category ChuCors. ...
doi:10.1080/03081079.2017.1349579
fatcat:kuifxt6ncvboboz73jrlo6p5ku
Chu Spaces, Concept Lattices, and Domains
2003
Electronical Notes in Theoretical Computer Science
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This paper serves to bring three independent but important areas of computer science to a common meeting point: Formal Concept Analysis (FCA), Chu Spaces, and Domain Theory (DT). ...
Among other results, we show that the notion of states in Scott's information system corresponds precisely to that of formal concepts in FCA with respect to all finite Chu spaces, and the entailment relation ...
Thanks go to Pascal Hitzler and John Pfaltz for stimulating discussions related to formal concept analysis, and to Austin Melton for pointers to Galois connections. ...
doi:10.1016/s1571-0661(03)50016-0
fatcat:lddnbglkhzbsxnvcnodeins3vq
Towards a Sequent Calculus for Formal Contexts
2016
European Conference on Artificial Intelligence
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This work focuses on the definition of a consequence relation between contexts with which we can decide whether certain contextual information is a logical consequence from a set of contexts considered ...
systems and the logical concept analysis [2, 9] . ...
The explicit construction of a general product (not necessarily either binary or nullary) is given below: Definition 6. ...
dblp:conf/ecai/KridloO16
fatcat:zmcdkd44bngdndjsjet34fibvu
Formal Concept Analysis and Structures Underlying Quantum Logics
[chapter]
2018
Communications in Computer and Information Science
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A Hilbert space H induces a formal context, the Hilbert formal context H, whose associated concept lattice is isomorphic to the lattice of closed subspaces of H. ...
In this paper, we continue with our study of the Chu construction by introducing the Chu correspondences between Hilbert contexts, and showing that the category of Propositional Systems, PropSys, is equivalent ...
This opens the way to future work oriented to the use of Chu correspondences to analyze more structures related to quantum logics, such as those in Abramsky's big toy models [1] . ...
doi:10.1007/978-3-319-91473-2_49
fatcat:rjwuwor6jnbtdgwmn4iz63tmha
OnL-fuzzy Chu correspondences
2011
International Journal of Computer Mathematics
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In this position paper, we focus on the framework of Chu correspondences extending Mori's approach [16] to formal concept analysis by proposing suitable definitions of the required concepts in an L-fuzzy ...
On the L-fuzzy generalization of Chu correspondences
Preliminaries We will assume that the reader is familiar with the standard notions of classical formal concept analysis [9] , such as context, formal ...
Soon after the introduction of "classical" formal concept analysis, a number of different approaches for its generalization were introduced and, nowadays, there are works which extend the theory with ideas ...
doi:10.1080/00207160903494147
fatcat:7gw7y75whbhw5nv2vfogzchxnm
Chu-Ren Huang, Nicoletta Calzolari, Aldo Gangemi, Alessandro Lenci, Alessandro Oltramari, and Laurent Prévot (eds.): Ontology and the Lexicon: a natural language processing perspective. (Studies in Natural Language Processing.)
2011
Language Resources and Evaluation
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In Chapt. 6, ''Experiments of ontology construction with Formal Concept Analysis'' (pp. 81-97, by SuJian Li, Qin Lu, and Wenjie Li), Formal Concept Analysis (FCA, where a mathematization of concepts and ...
their hierarchy allows for the analysis of conceptual data) is used to derive an ontology for a set of prespecified ontology concepts. ...
doi:10.1007/s10579-011-9138-z
fatcat:zzpds2z2qves5aoto4vbl5rue4
Formal Topology, Chu Space and Approximable Concept
2005
International Conference on Concept Lattices and their Applications
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Wille initiated formal concept analysis, which is an order-theoretical analysis of scientific data. Concept is one of the main notions and tools. ...
Zhang considered a special form of Chu space, and introduced the notion of approximable concept in [3, 9, 10], which is a generalization of concept. These are two "parallel worlds". ...
Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 10471035/A010104) and Natural Science Foundation of Shandong Province (Grant No. 2003ZX13). ...
dblp:conf/cla/ChenL05
fatcat:c7wtkcypizg4tak2c677gasywa
Revising the link between L-Chu correspondences and completely lattice L-ordered sets
2014
Annals of Mathematics and Artificial Intelligence
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Continuing our categorical study of L-fuzzy extensions of formal concept analysis, we provide a representation theorem for the category of L-Chu correspondences between L-formal contexts and prove that ...
. ≈ and the following holds: ...
Introduction This paper deals with an extremely general form of Formal Concept Analysis (FCA) based on categorical constructs and L-fuzzy sets. ...
doi:10.1007/s10472-014-9416-8
fatcat:7qzbq5kxone2vfjg2d7hrwwasu
Formal concept analysis of higher order
2016
International Journal of General Systems
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The paper provides a method how to compute such second order formal concepts by using of bonds between external formal contexts or by using of heterogeneous formal contexts methods. ...
Last part of the paper shows how this structure generalizes homogenic fuzzy formal context and its derivation operators. ...
Bonds and Chu correspondences FCA provides the useful methods how to connect two formal contexts. ...
doi:10.1080/03081079.2015.1072924
fatcat:q3sbkszi6rdi7eqbfpxshnaxoa
Lattice-Valued Topological Systems as a Framework for Lattice-Valued Formal Concept Analysis
2013
Journal of Mathematics
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Recently, Denniston, Melton, and Rodabaugh presented a new categorical outlook on a certain lattice-valued extension of Formal Concept Analysis (FCA) of Ganter and Wille; their outlook was based on the ...
This paper extends the approach of Denniston et al. clarifying the relationships between Chu spaces of Pratt, many-valued formal contexts of FCA, lattice-valued interchange systems, and Galois connections ...
Rodabaugh (Youngstown State University) for going through the draft version of the paper, pointing out its various deficiencies and suggesting their adjustments. ...
doi:10.1155/2013/506275
fatcat:vb7wuu2h4ze25irsy6alevwpa4
Page 2889 of Mathematical Reviews Vol. , Issue 2001E
[page]
2001
Mathematical Reviews
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Summary: “In this note we first formalize the notion of hard tautologies using a nondeterministic generalization of instance complexity. ...
Summary: “Chu spaces, which derive from the Chu construct of *-autonomous categories, can be used to represent most math- ematical structures. Moreover, the logic of Chu spaces is linear logic. ...
Chu connections and back diagonals betweenQ-distributors
2016
Journal of Pure and Applied Algebra
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2015 pre-print arXiv:1503.06647v3 fatcat:ij4vbu4mmjfopmfcjyl6gt25riOther Versions
As an application of Chu connections, a postulation of the intuitive idea of reduction of formal contexts in the theory of formal concept analysis is presented, and a characterization of reducts of formal ...
These notions, meaningful for closed bicategories, dualize the constructions of arrow categories and the Freyd completion of categories. ...
The second and the third authors acknowledge the support of National Natural Science Foundation of China (11371265). We thank the anonymous referee for several helpful remarks. ...
doi:10.1016/j.jpaa.2015.10.005
fatcat:dbb7hqqkavhrhcoykd7q42lq64
Page 7605 of Mathematical Reviews Vol. , Issue 2004j
[page]
2004
Mathematical Reviews
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In computable analysis, these notions are generalized to closed subsets of Eu- clidean space using their metric distance functions. ...
The authors study a further generalization of these concepts to computable metric spaces. ...
Viral Logical Concept Analysis for Malware Conceptual Hierarchy Generation
2017
International Journal of Machine Learning and Computing
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In this paper, we introduce an approach using Formal Concept Analysis (FCA) to generate a malware hierarchy. ...
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. ...
Formal Concept Analysis Formal Concept Analysis [7] is a data analysis technique aiming at recognizing formal concepts of a formal context and constructing a concept lattice accordingly. ...
doi:10.18178/ijmlc.2017.7.4.619
fatcat:oiwanqmljbbubkyyrm7o2m6hp4
A mosaic of Chu spaces and Channel Theory with applications to Object Identification and Mereological Complexity
[article]
2018
arXiv
pre-print
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Chu Spaces and Channel Theory are well established areas of investigation in the general context of category theory. ...
We review a range of examples and applications of these methods in logic and computer science, including Formal Concept Analysis, distributed systems and ontology development. ...
Formal Concept Analysis and Computation in Chu spaces Category theory can be viewed as a unified language for handling conceptual complexities in both mathematics and computer science. ...
arXiv:1803.08874v1
fatcat:5rslhaxjtzb4debu7qlr3ir7yq
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