Schauder Hats for the Two-Variable Fragment of BL

Abstract

The theory of Schauder hats is a beautiful and powerful tool for investigating, under several respects, the algebraic semantics of Łukasiewicz infinite-valued logic [CDM99],[MMM07], [Mun94], [P95]. As a notably application of the theory, the elements of the free n-generated MV-algebra, that constitutes the algebraic semantics of the n-variate fragment ofŁukasiewicz logic, are obtained as (t-conorm) monoidal combination of finitely many hats, which are in turn obtained through finitely many applications of an operation called starring, starting from a finite family of primitive hats. The aim of this paper is to extend this portion of the Schauder hats theory to the two-variable fragment of Hajek’s Basic logic. This step represents a non-trivial generalization of the one variable case studied in [AG05], [Mon00], and provides sufficient insight to capture the behaviour of the n-variable case for n ≥ 1.