3 papers
math.LO2026
Computable Quantification in Reflective Grounded Arithmetic
Bryan Ford
Informal statements of Gödel's incompleteness theorems often run: "no consistent formal system with arithmetic can be complete" - omitting the fact that the theorems as proved ass…
cs.PL2026
Have a thing? Reasoning around recursion with dynamic typing in grounded arithmetic
Dimitrios Alexopoulos, Elliot Bobrow, Bryan Ford +5
Neither the classical nor intuitionistic logic traditions are perfectly aligned with the purpose of reasoning about computation, as neither can permit unconstrained recursive defin…
math.LO2025
Reasoning Around Paradox with Grounded Deduction
Bryan Ford
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…