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Boolos’s Curious Inference in Isabelle/HOL

Ketland, Jeffrey (2022) Boolos’s Curious Inference in Isabelle/HOL. Archive of Formal Proofs.

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Abstract

In 1987, George Boolos gave an interesting and vivid concrete example
of the considerable speed-up afforded by higher-order logic over
first-order logic. (A phenomenon first noted by Kurt Gödel in 1936.)
Boolos’s example concerned an inference I with five premises, and a
conclusion, such that the shortest derivation of the conclusion from
the premises in a standard system for first-order logic is astronomically
huge; while there exists a second-order derivation whose length
is of the order of a page or two. Boolos gave a short sketch of that
second-order derivation, which relies on the comprehension principle
of second-order logic. Here, Boolos’s inference is formalized into fourteen
lemmas, each quickly verified by the automated-theorem-proving
assistant Isabelle/HOL.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Ketland, Jeffreyjeffreyketland@gmail.com0000-0002-5128-4387
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Computer Science
Depositing User: Dr Jeffrey Ketland
Date Deposited: 07 Jul 2022 16:40
Last Modified: 07 Jul 2022 16:40
Item ID: 20849
Journal or Publication Title: Archive of Formal Proofs
Official URL: https://www.isa-afp.org/entries/Boolos_Curious_Inf...
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Computer Science
Date: 4 July 2022
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/20849

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