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The Chu construction and generalized formal concept analysis

L. Antoni, I. P. Cabrera, S. Krajči, O. Krídlo, M. Ojeda-Aciego
2017 International Journal of General Systems  
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

Guo-Qiang Zhang
2003 Electronical Notes in Theoretical Computer Science  
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

Ondrej Kridlo, Manuel Ojeda-Aciego
2016 European Conference on Artificial Intelligence  
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]

Ondrej Krídlo, Manuel Ojeda-Aciego
2018 Communications in Computer and Information Science  
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

Ondrej Krídlo, M. Ojeda-Aciego
2011 International Journal of Computer Mathematics  
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.)

Andrea C. Schalley
2011 Language Resources and Evaluation  
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

Xueyou Chen, Qingguo Li
2005 International Conference on Concept Lattices and their Applications  
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

Ondrej Krídlo, Manuel Ojeda-Aciego
2014 Annals of Mathematics and Artificial Intelligence  
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

Ondrej Krídlo, Stanislav Krajči, Lubomir Antoni
2016 International Journal of General Systems  
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

Sergey A. Solovyov
2013 Journal of Mathematics  
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  
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

Lili Shen, Yuanye Tao, Dexue Zhang
2016 Journal of Pure and Applied Algebra  
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  
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

Nguyen Thien Binh
2017 International Journal of Machine Learning and Computing  
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]

Chris Fields, James F. Glazebrook
2018 arXiv   pre-print
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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