Truth-depressing hedges and BL-logic (Q853470)

Basic logic was introduced by Hájek as the logic of continuous t-norms and their adjoint implications. BL-algebras are the algebras of basic logic. To capture the notion of ``slightly true'', in this paper propositional basic logic is extended by adding a suitable unary connective. In a sense this is dual to Hájek's connective for ``very true''. A complete axiomatization is given, and various examples are discussed.