dorsal/arxiv
View SchemaTurning the Liar paradox into a metatheorem of Basic logic
| Authors | Paola A. Zizzi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0701171 |
| URL | https://arxiv.org/abs/quant-ph/0701171 |
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.
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"abstract": "We show that self-reference can be formalized in Basic logic by means of the\nnew connective @, called \"entanglement\". In fact, the property of\nnon-idempotence of the connective @ is a metatheorem, which states that a\nself-entangled sentence loses its own identity. This prevents having\nself-referential paradoxes in the corresponding metalanguage. In this context,\nwe introduce a generalized definition of self-reference, which is needed to\ndeal with the multiplicative connectives of substructural logics.",
"arxiv_id": "quant-ph/0701171",
"authors": [
"Paola A. Zizzi"
],
"categories": [
"quant-ph",
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"title": "Turning the Liar paradox into a metatheorem of Basic logic",
"url": "https://arxiv.org/abs/quant-ph/0701171"
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