A Finite State Model for On-Line Analytical Processing in Triadic Contexts

This paper discusses how traditional line diagrams of standard (dyadic) concept lattices can be used for exploring and navigating triadic data, and uses the formalisms of finite state machines for modeling the navigation patterns a user might follow.

Abstract

About ten years ago, triadic contexts were presented by Lehmann and Wille as an extension of Formal Concept Analysis. However, they have rarely been used up to now, which may be due to the rather complex structure of the resulting diagrams. In this paper, we go one step back and discuss how traditional line diagrams of standard (dyadic) concept lattices can be used for exploring and navigating triadic data. Our approach is inspired by the slice & dice paradigm of On-Line-Analytical Processing (OLAP).We recall the basic ideas of OLAP, and showhowthey may be transferred to triadic contexts. For modeling the navigation patterns a user might follow, we use the formalisms of finite state machines. In order to present the benefits of our model, we show how it can be used for navigating the IT Baseline Protection Manual of the German Federal Office for Information Security.