Turning the Liar paradox into a metatheorem of Basic logic
<|reference_start|>Turning the Liar paradox into a metatheorem of Basic logic: 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.<|reference_end|>
@article{zizzi2007turning,
    title={Turning the Liar paradox into a metatheorem of Basic logic},
    author={Paola A. Zizzi},
    journal={arXiv preprint arXiv:quant-ph/0701171},
    year={2007},
    archivePrefix={arXiv},
    eprint={quant-ph/0701171},
    primaryClass={quant-ph cs.LO math.LO}
}