Infinite contexts and their corresponding lattices are of theoretical and practical interest since they may o#er 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].

We present an innovative approach to information retrieval for domain-specific 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 domain-specific concept hierarchies using FCA, and (4) incorporates the learnt concept hierarchies and WordNet for content-based 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 non-trivial 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.

Abstract. Web-menu is one of the most important and widely used modalities in Human-Computer 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 multi-layered 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 web-menu layouts and the ones generated using FCA: many of today’s web-menu hierarchies are tree structures in which submenus do not overlap, while menu-hierarchies obtained using FCA are part of a lattice structure in which sub-menus are not required to be mutually exclusive. FcAWN is one of the few semi-automated web-menu design methods with which one can construct consistent and logical menu hierarchies for web navigation. 1

Abstract. Menu-hierarchy is an important mechanism for human-computer 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 navigation-menu design [32], where lattice theory [1] provides the mathematical basis for menu-structures while the user-interface remains unchanged. Implemented in Java and Perl, our experimental prototype has the following features: (a) automated generation of folder hierarchy; (b) automatic folder-name assignment; (c) pruning for global folder-depth control; (d) lattice-unfolding to obtain trees that allow for backing-up. 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 hyper-link navigation hierarchy in a couple of minutes based on a ten attribute set; a desktop web-browser is used to test and validate the hierarchy. The basic idea of ACOSys comes from our recognition that menu-structures can be regarded as mathematical structures in the abstract sense and, in return, they can benefit from an order-theoretic investigation. An additional recognition is that tree-structures are important to facilitate the backing-up operation for folder hierarchies, but the tension between trees and lattices can be resolved by unfolding lattices to trees. 1

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 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. 1