Towards galois connections over positive semifields

Abstract

In this paper we try to extend the Galois connection construction of K-Formal Concept Analysis to handle semifields which are not idempotent. Important examples of such algebras are the extended non-negative reals and the extended non-negative rationals, but we provide a construction that suggests that such semifields are much more abundant than suspected. This would broaden enormously the scope and applications of K-Formal Concept Analysis.