Turning the Liar paradox into a metatheorem of Basic logic

Abstract

We show that self-reference can be formalized in Basic logic by means of the new connective @, called "entanglement". In fact, the property of non-idempotence of the connective @ is a metatheorem, which states that a self-entangled sentence loses its own identity. This prevents having self-referential paradoxes in the corresponding metalanguage. In this context, we introduce a generalized definition of self-reference, which is needed to deal with the multiplicative connectives of substructural logics.