Reasoning Around Paradox with Grounded Deduction
<|reference_start|>Reasoning Around Paradox with Grounded Deduction: How can we reason around logical paradoxes without falling into them? This paper introduces grounded deduction or GD, a Kripke-inspired approach to first-order logic and arithmetic that is neither classical nor intuitionistic, but nevertheless appears both pragmatically usable and intuitively justifiable. GD permits the direct expression of unrestricted recursive definitions - including paradoxical ones such as 'L := not L' - while adding dynamic typing premises to certain inference rules so that such paradoxes do not lead to inconsistency. This paper constitutes a preliminary development and investigation of grounded deduction, to be extended with further elaboration and deeper analysis of its intriguing properties.<|reference_end|>
@article{ford2024reasoning,
    title={Reasoning Around Paradox with Grounded Deduction},
    author={Bryan Ford},
    journal={arXiv preprint arXiv:2409.08243},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.08243},
    primaryClass={math.LO cs.LO}
}