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A cartesian closed category of approximable concept structures
 Proceedings of the International Conference On Conceptual Structures
, 2004
"... Abstract. Infinite contexts and their corresponding lattices are of theoretical and practical interest since they may offer connections with and insights from other mathematical structures which are normally not restricted to the finite cases. In this paper we establish a systematic connection betwe ..."
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Abstract. Infinite contexts and their corresponding lattices are of theoretical and practical interest since they may offer connections with and insights from other mathematical structures which are normally not restricted to the finite cases. In this paper we establish a systematic connection between formal concept analysis and domain theory as a categorical equivalence, enriching the link between the two areas as outlined in [25]. Building on a new notion of approximable concept introduced by Zhang and Shen [26], this paper provides an appropriate notion of morphisms on formal contexts and shows that the resulting category is equivalent to (a) the category of complete algebraic lattices and Scott continuous functions, and (b) a category of information systems and approximable mappings. Since the latter categories are cartesian closed, we obtain a cartesian closed category of formal contexts that respects both the context structures as well as the intrinsic notion of approximable concepts at the same time. 1
Default reasoning over domains and concept hierarchies
 In Proceedings of the 27th German conference on Artificial Intelligence (KI04
, 2004
"... Abstract. 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 wit ..."
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Abstract. 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. 1
Bootstrapping ontology learning for information retrieval using formal concept analysis and information anchors
 14TH INTERNATIONAL CONFERENCE ON CONCEPTUAL STRUCTURES
"... We present an innovative approach to information retrieval for domainspecific digital library collections. We use a combination of Formal Concept Analysis (FCA) and a notion of information anchors to facilitate information delivery to the end user. This approach (1) uses ranked objects in attribut ..."
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We present an innovative approach to information retrieval for domainspecific digital library collections. We use a combination of Formal Concept Analysis (FCA) and a notion of information anchors to facilitate information delivery to the end user. This approach (1) uses ranked objects in attribute concepts to facilitate topical queries for experts and expertise profiles; (2) formulates (keyword by keyword) context for concept lattice construction via a set of heuristics, including those based on information anchors for selecting descriptive phrases, (3) bootstraps the learning of domainspecific concept hierarchies using FCA, and (4) incorporates the learnt concept hierarchies and WordNet for contentbased document classification. To demonstrate the feasibility and utility of this approach, we implemented a prototype online information retrieval systemmemsworldonline.case.edu (MWOL) for the emerging engineering discipline of MEMS (microelectromechanical systems) incorporating these ideas. MWOL has been actively used by a nontrivial group of MEMS practitioners; all user queries are processed in a fraction of a second as a result of inverse indexing strategy using Berkeley DB. Voluntary user feedback using online forms has been encouraging. However, no other systems with similar features are available for a comparative study at this point.
Faster Concept Analysis
"... Abstract. We introduce a simple but efficient, multistage algorithm for constructing concept lattices (MCA). A concept lattice can be obtained as the closure system generated from attribute concepts (dually, object concepts). There are two strategies to use this as the basis of an algorithm: (a) for ..."
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Abstract. We introduce a simple but efficient, multistage algorithm for constructing concept lattices (MCA). A concept lattice can be obtained as the closure system generated from attribute concepts (dually, object concepts). There are two strategies to use this as the basis of an algorithm: (a) forming intersections by joining one attribute concept at a time, and (b) repeatedly forming pairwise intersections starting from the attribute concepts. A straightforward translation of (b) to an algorithm suggests that pairwise intersection be performed among all cumulated concepts. MCA is parsimonious in forming the pairwise intersections: it only performs such operations among the newly formed concepts from the previous stage, instead of cumulatively. We show that this parsimonious multistage strategy is complete: it generates all concepts. To make this strategy really work, one must overcome the need to eliminate duplicates (and potentially save time even further), since concepts generated at a later stage may have already appeared in one of the earlier stages. As considered in several other algorithms in the literature [5], we achieve this by an auxiliary search tree which keeps all existing concepts as paths from the root to a flagged node or a leaf. The depth of the search tree is bounded by the total number of attributes, and hence the time complexity for concept lookup is bounded by the logarithm of the total number of concepts. For constructing lattice diagrams, we adapt a subquadratic algorithm of Pritchard [9] for computing subset partial orders to constructing the Hasse diagrams. Instead of the standard expected quadratic complexity, the Pritchard approach achieves a worstcase time O(N 2 /log N). Our experimental results showed significant improvements in speed for a variety of input profiles against three leading algorithms considered in the comprehensive comparative study [5]: Bordat, Chein, and Norris. 1
Concept analysis as a formal method for menu design
 Lecture Notes in Computer Science
"... Abstract. The design and construction of navigation menus for websites have traditionally been performed manually according to the intuition of a web developer. This paper introduces a new approach, FcAWN (pronounced “fawn”) – Formal concept Analysis for Web Navigation – to assist in the design and ..."
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Abstract. The design and construction of navigation menus for websites have traditionally been performed manually according to the intuition of a web developer. This paper introduces a new approach, FcAWN (pronounced “fawn”) – Formal concept Analysis for Web Navigation – to assist in the design and generation of a coherent and logical navigation hierarchy for a set of web documents. We provide an algorithmic process for generating multilayered menu models using FcAWN and demonstrate its feasibility with an experimental case study. Our study reveals a fundamental difference between the traditional treebased menu structure and the latticebased menu structure by FcAWN: a FcAWNgenerated lattice structure is more general than a tree structure and yet is mathematically sound and uniquely suited for menu design and construction. FcAWN is the first mathematical principle for menu design and generation, providing a practical basis for humancomputer interaction. 1
CRLChu correspondences
"... Abstract. We continue our study of the general notion of LChu correspondence by introducing the category CRLChuCors incorporating residuation to the underlying complete lattice L, specifically, on the basis of a residuationpreserving isotone Galois connection λ. Then, the Lbonds are generalized ..."
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Abstract. We continue our study of the general notion of LChu correspondence by introducing the category CRLChuCors incorporating residuation to the underlying complete lattice L, specifically, on the basis of a residuationpreserving isotone Galois connection λ. Then, the Lbonds are generalized within this same framework, and its structure is related to that of the extent of a suitably defined λdirect product. 1
FcAWN: Concept Analysis as a Formal Method for Automated WebMenu Design
 Conceptual Structures at Work, Shaker Verlag
, 2004
"... Abstract. Webmenu is one of the most important and widely used modalities in HumanComputer Interaction (HCI). The design and construction of navigation menus for websites, however, have traditionally been left to the intuition of a web developer. This paper proposes the use of a mathematical theor ..."
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Abstract. Webmenu is one of the most important and widely used modalities in HumanComputer Interaction (HCI). The design and construction of navigation menus for websites, however, have traditionally been left to the intuition of a web developer. This paper proposes the use of a mathematical theory called Formal Concept Analysis (FCA) [5, 9, 14, 16, 17] to assist in the design and automatic generation of a navigation hierarchy for a set of web documents. We demonstrate how multilayered menu models can be devised and automatically generated by an adaptation and application of the principle of FCA and its associated algorithms. Our approach, FcAWN (pronounced fawn) – Formal concepts Applied to Web Navigation – reveals a fundamental difference between existing webmenu layouts and the ones generated using FCA: many of today’s webmenu hierarchies are tree structures in which submenus do not overlap, while menuhierarchies obtained using FCA are part of a lattice structure in which submenus are not required to be mutually exclusive. FcAWN is one of the few semiautomated webmenu design methods with which one can construct consistent and logical menu hierarchies for web navigation. 1
ACOSys: An Experimental System for Automated Content Organization
"... Abstract. Menuhierarchy is an important mechanism for humancomputer interaction. In this paper we report the design, prototyping, and experiences of an experimental system called ACOSys for automated organization of contents by menu/folder hierarchies. ACOSys is built on a similar principle of our ..."
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Abstract. Menuhierarchy is an important mechanism for humancomputer interaction. In this paper we report the design, prototyping, and experiences of an experimental system called ACOSys for automated organization of contents by menu/folder hierarchies. ACOSys is built on a similar principle of our other work, FcAWN – formal concept analysis for web navigationmenu design [32], where lattice theory [1] provides the mathematical basis for menustructures while the userinterface remains unchanged. Implemented in Java and Perl, our experimental prototype has the following features: (a) automated generation of folder hierarchy; (b) automatic foldername assignment; (c) pruning for global folderdepth control; (d) latticeunfolding to obtain trees that allow for backingup. An experiment study is performed for ACOSys to generate an organization of the Medlars collection, an archive of 1039 medical articles commonly used for information retrieval benchmarking. ACOSys created a hyperlink navigation hierarchy in a couple of minutes based on a ten attribute set; a desktop webbrowser is used to test and validate the hierarchy. The basic idea of ACOSys comes from our recognition that menustructures can be regarded as mathematical structures in the abstract sense and, in return, they can benefit from an ordertheoretic investigation. An additional recognition is that treestructures are important to facilitate the backingup operation for folder hierarchies, but the tension between trees and lattices can be resolved by unfolding lattices to trees. 1
Proceedings of the TwentyThird International Joint Conference on Artificial Intelligence Granular Description of Qualitative Change
"... Qualitative representations of spatial knowledge have been widely studied and a variety of frameworks are used to express relationships between static regions. Dynamic regions present a much greater challenge, but are important in practical applications such as describing crowds of people moving ove ..."
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Qualitative representations of spatial knowledge have been widely studied and a variety of frameworks are used to express relationships between static regions. Dynamic regions present a much greater challenge, but are important in practical applications such as describing crowds of people moving over time. Previous work has analysed changes as regions merge and split and as new regions are created and existing ones disappear. We present a novel framework for the qualitative description of spatial regions based on two levels of granularity. Introducing granularity yields significantly more informative qualitative descriptions than are available from a single level of detail. The formal model represents a region, which may have multiple components, as a bipartite graph where the nodes are the components of the region at a fine level of detail and at a coarse level. The edges of the graph model the way that a component in the coarse view can be made up of parts of components at the more detailed level. We show that all graphs of this form (except for some degenerate cases) can be realized as regions in a discrete space of pixels, and we develop a theory of relations between these graphs to model the dynamic behaviour of regions. 1
Annals of Mathematics and Artificial Intelligence manuscript No. (will be inserted by the editor) Congruence
, 2008
"... relations on some hyperstructures ..."
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