5 papers
Idealizing Useful Fictions in Omega Grounded Arithmetic
Bryan Ford
Grounded arithmetic is a family of formal systems for reasoning about computation in which a statement may be asserted only when a terminating computation backs it; the logics are…
Internal Reasoning and Consistency in Reflective Grounded Arithmetic
Bryan Ford
Reflective Grounded Arithmetic (RGA) is a paracomplete arithmetic allowing direct expression of any general-recursive computation. Every RGA term is a program and truth is grounded…
Computable Quantification in Reflective Grounded Arithmetic
Bryan Ford
Informal statements of Gödel's incompleteness theorems often run: "any consistent formal system with arithmetic has true but unprovable statements." That reading assumes a classica…
Have a thing? Reasoning around recursion with dynamic typing in grounded arithmetic
Dimitrios Alexopoulos, Elliot Bobrow, Yusuf Demir +4
Neither the classical nor intuitionistic logic traditions are perfectly aligned with the purpose of reasoning about computation, as neither can permit unconstrained recursive defin…
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…