Canonical extensions, Duality theory, and
             Formal Concept Analysis

                                      Mai Gehrke

                     LIAFA CNRS – University of Paris 7, France

Abstract. The theory of canonical extensions, developed by Jonsson and Tarski in the
setting of Boolean algebras with operators, provides an algebraic approach to duality
theory. Recent developments in this theory have revealed that in this algebraic guise
duality theory is no more complicated outside than within the setting of Boolean
algebras or distributive lattices. This has opened the possibility of exporting the highly
developed machinery and knowledge available in the classical setting (e.g. in modal
logic) to the completely general setting of partially ordered and non-distributive lattice
ordered algebras. Duality theory in this setting is a special instance of the connection
between formal contexts and concept lattices and thus allows methods of classical
algebraic logic to be imported into FCA.

This will be an introductory talk on the subject of canonical extensions with the
purpose of outlining the relationship between the three topics of the title.