Expanding Basic Fuzzy Logic with truth constants for component delimiters

In this paper we investigate the propositional logic of standard algebras for Hájek's Basic Fuzzy Logic BL in a language expanded with propositional constants for the idempotent elements delimiting the Ł-, G-, and Π-components of the algebra. We start from a fixed standard BL-algebra; introduce new propositional constants; present a suitable set of axioms; investigate completeness results; and give some complexity results.