Gongqin Shen | Case Western Reserve University (original) (raw)
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This paper serves to bring three independent but important areas of computer science to a common ... more 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). Each area is given a perspective or reformulation that is conducive to the flow of ideas and to the exploration of cross-disciplinary connections. Among other results, we show that the notion of state 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 corresponds to "association rules". We introduce, moreover, the notion of approximable concept and show that approximable concepts represent algebraic lattices which are identical to Scott domains except the inclusion of a top element. This notion serves as a stepping stone in the recent work in which a new notion of morphism on formal contexts results in a category equivalent to (a) the category of complete algebraic lattices and Scott continuous functions, and (b) a category of information systems and approximable mappings.
... GQ Zhang1, Gongqin Shen1, Josh Staiger1, Adam Troy1, and Jiayang Sun2 1 Department of Electri... more ... GQ Zhang1, Gongqin Shen1, Josh Staiger1, Adam Troy1, and Jiayang Sun2 1 Department of Electrical Engineering and Computer Science 2 Department of Statistics Case Western Reserve University, Cleveland, Ohio, USA gqz@eecs.case.edu, http://newton.case.edu ...
The design and construction of navigation menus for websites have traditionally been performed ma... more 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 multi-layered menu models using FcAWN and demonstrate its feasibility with an experimental case study. Our study reveals a fundamental difference between the traditional tree-based menu structure and the lattice-based menu structure by FcAWN: a FcAWN-generated 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 human-computer interaction.
THEORY AND APPLICATIONS OF CATEGORIES, 2006
Page 1. ISSN 1201-561X TAC 6 THEORY AND APPLICATIONS OF CATEGORIES Volume 17, 2006-07 A special v... more Page 1. ISSN 1201-561X TAC 6 THEORY AND APPLICATIONS OF CATEGORIES Volume 17, 2006-07 A special volume: Chu spaces: theory and applications* Preface The guest editors 1 The Chu construction: history of an idea Michael Barr 10 Coherence of the double involution on *-autonomous categories JRB Cockett, M. Hasegawa and RAG Seely 17 A Parigot-style linear λ-calculus for full intuitionistic linear Valeria de Paiva and Eike Ritter 30 The Dialectica interpretation of first-order classical affine logic Masaru Shirahata 49 ...
This paper serves to bring three independent but important areas of computer science to a common ... more 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). Each area is given a perspective or reformulation that is conducive to the flow of ideas and to the exploration of cross-disciplinary connections. Among other results, we show that the notion of state 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 corresponds to "association rules". We introduce, moreover, the notion of approximable concept and show that approximable concepts represent algebraic lattices which are identical to Scott domains except the inclusion of a top element. This notion serves as a stepping stone in the recent work in which a new notion of morphism on formal contexts results in a category equivalent to (a) the category of complete algebraic lattices and Scott continuous functions, and (b) a category of information systems and approximable mappings.
... GQ Zhang1, Gongqin Shen1, Josh Staiger1, Adam Troy1, and Jiayang Sun2 1 Department of Electri... more ... GQ Zhang1, Gongqin Shen1, Josh Staiger1, Adam Troy1, and Jiayang Sun2 1 Department of Electrical Engineering and Computer Science 2 Department of Statistics Case Western Reserve University, Cleveland, Ohio, USA gqz@eecs.case.edu, http://newton.case.edu ...
The design and construction of navigation menus for websites have traditionally been performed ma... more 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 multi-layered menu models using FcAWN and demonstrate its feasibility with an experimental case study. Our study reveals a fundamental difference between the traditional tree-based menu structure and the lattice-based menu structure by FcAWN: a FcAWN-generated 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 human-computer interaction.
THEORY AND APPLICATIONS OF CATEGORIES, 2006
Page 1. ISSN 1201-561X TAC 6 THEORY AND APPLICATIONS OF CATEGORIES Volume 17, 2006-07 A special v... more Page 1. ISSN 1201-561X TAC 6 THEORY AND APPLICATIONS OF CATEGORIES Volume 17, 2006-07 A special volume: Chu spaces: theory and applications* Preface The guest editors 1 The Chu construction: history of an idea Michael Barr 10 Coherence of the double involution on *-autonomous categories JRB Cockett, M. Hasegawa and RAG Seely 17 A Parigot-style linear λ-calculus for full intuitionistic linear Valeria de Paiva and Eike Ritter 30 The Dialectica interpretation of first-order classical affine logic Masaru Shirahata 49 ...