Reasoning Around Paradox with Grounded Deduction
Logic
2025-04-07 v4 Logic in Computer Science
Abstract
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.
Keywords
Cite
@article{arxiv.2409.08243,
title = {Reasoning Around Paradox with Grounded Deduction},
author = {Bryan Ford},
journal= {arXiv preprint arXiv:2409.08243},
year = {2025}
}