Computing with conceptual structures

Abstract

We give an overview over the computational tools for conceptional structures that have emerged from the theory of Formal Concept Analysis, with emphasis on basic ideas rather than technical details. We describe what we mean by conceptual computations, and try to convice the reader that an elaborate formalization is a necessary precondition. Claiming that Formal Concept Analysis provides such a formal background, we present as examples two well known algorithms in very simple pseudo code. These can be used for navigating in a lattice, thereby supporting some prototypical tasks of conceptual computation. We refer to some of the many more advanced methods, discuss how to compute with limited precision and explain why in the case of incomplete knowledge the conceptual approach is more efficient than a combinatorial one. Utilizing this efficiency requires skillful use of the formalism. We present two results that lead in this direction.