Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Quantum Physics

arXiv:quant-ph/0701171 (quant-ph)
[Submitted on 23 Jan 2007 (v1), last revised 28 Mar 2007 (this version, v2)]

Title:Turning the Liar paradox into a metatheorem of Basic logic

Authors:Paola A. Zizzi
View PDF
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.
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
Subjects: Quantum Physics (quant-ph); Logic in Computer Science (cs.LO); Logic (math.LO)
Cite as: arXiv:quant-ph/0701171
  (or arXiv:quant-ph/0701171v2 for this version)
  https://doi.org/10.48550/arXiv.quant-ph/0701171

Submission history

From: Paola Zizzi [view email]
[v1] Tue, 23 Jan 2007 18:36:47 UTC (104 KB)
[v2] Wed, 28 Mar 2007 11:53:27 UTC (12 KB)
Full-text links:

Access Paper:

view license
Current browse context:
quant-ph
< prev   |   next >
new | recent | 2007-01

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)