2007/01/23 by Paola Zizzi, Paola A. Zizzi, Zizzi, Paola A.
Computer Science · Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Logic (math.LO) #Logic in Computer Science (cs.LO) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #cs.LO #math.LO #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0701171
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
openalex publication_date 2007/01/23 · arxiv created 2007/03/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.