Turning the Liar paradox into a metatheorem of Basic logic
Quantum Physics
2007-05-23 v2 Logic in Computer Science
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.
Cite
@article{arxiv.quant-ph/0701171,
title = {Turning the Liar paradox into a metatheorem of Basic logic},
author = {Paola A. Zizzi},
journal= {arXiv preprint arXiv:quant-ph/0701171},
year = {2007}
}
Comments
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