Turning the Liar paradox into a metatheorem of Basic logic
Abstract
Description
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.
12 pages, 1 figure, submitted to CIE 2007. The subject of Section 4, formerly devoted to the conclusions, has been changed, and is about a generalized version of self-reference
12 pages, 1 figure, submitted to CIE 2007. The subject of Section 4, formerly devoted to the conclusions, has been changed, and is about a generalized version of self-reference