Consistent ultrafinitist logic

06/24/2021
by   Michał J. Gajda, et al.
0

Ultrafinitism postulates that we can only compute on relatively short objects, and numbers beyond certain value are not available. This approach would also forbid many forms of infinitary reasoning and allow to remove certain paradoxes stemming from enumeration theorems. However, philosophers still disagree of whether such a finitist logic would be consistent. We present preliminary work on a proof system based on Curry-Howard isomorphism. We also try to present some well-known theorems that stop being true in such systems, whereas opposite statements become provable. This approach presents certain impossibility results as logical paradoxes stemming from a profligate use of transfinite reasoning.

READ FULL TEXT

Authors

page 1

page 2

page 3

page 4

07/16/2002

Interpolation Theorems for Nonmonotonic Reasoning Systems

Craig's interpolation theorem (Craig 1957) is an important theorem known...
01/28/2020

First-Order Logic for Flow-Limited Authorization

We present the Flow-Limited Authorization First-Order Logic (FLAFOL), a ...
08/21/2019

Free Theorems Simply, via Dinaturality

Free theorems are a popular tool in reasoning about parametrically polym...
12/24/2019

A Promise Theoretic Account of the Boeing 737 Max MCAS Algorithm Affair

Many public controversies involve the assessment of statements about whi...
01/16/2014

Automated Search for Impossibility Theorems in Social Choice Theory: Ranking Sets of Objects

We present a method for using standard techniques from satisfiability ch...
01/03/2022

Formalising Geometric Axioms for Minkowski Spacetime and Without-Loss-of-Generality Theorems

This contribution reports on the continued formalisation of an axiomatic...
01/23/2021

Calculating a backtracking algorithm: an exercise in monadic program derivation

Equational reasoning is among the most important tools that functional p...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.