Features of Interaction Between Formal Concept Analysis and Algebraic Geometry

Abstract

This paper contributes to Algebraic Concept Analysis by examining connections between Formal Concept Analysis and Algebraic Geometry. The investigations are based on polynomial contexts (over a field K in n variables) which are defined by ${\mathbb{K}}^{(n)} := (K^n,K[x_1,\ldots,x_n],\perp)$ where $a \perp f :\Leftrightarrow f(a)=0$ for a ∈ K ⁿ and any polynomial f∈ K[x ₁,...,x _n ]. Important notions of Algebraic Geometry such as algebraic varieties, coordinate algebras, and polynomial morphisms are connected to notions of Formal Concept Analysis. That allows to prove many interrelating results between Algebraic Geometry and Formal Concept Analysis, even for more abstract notions such as affine and projective schemes.

This paper is an adapted version of the first part of [Be99]