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.

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. 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