Journal of Automated Reasoning

, Volume 52, Issue 4, pp 361–378

Using Isabelle/HOL to Verify First-Order Relativity Theory

Article

Abstract

Logicians at the Rényi Mathematical Institute in Budapest have spent several years developing versions of relativity theory (special, general, and other variants) based wholly on first-order logic, and have argued in favour of the physical decidability, via exploitation of cosmological phenomena, of formally unsolvable questions such as the Halting Problem and the consistency of set theory. As part of a joint project, researchers at Sheffield have recently started generating rigorous machine-verified versions of the Hungarian proofs, so as to demonstrate the soundness of their work. In this paper, we explain the background to the project and demonstrate a first-order proof in Isabelle/HOL of the theorem “no inertial observer can travel faster than light”. This approach to physical theories and physical computability has several pay-offs, because the precision with which physical theories need to be formalised within automated proof systems forces us to recognise subtly hidden assumptions.

Keywords

Isabelle/HOL First-order relativity theory Hypercomputation Physics and computation 

CR Subject Classification

F.4.1 J.2 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of SheffieldSheffieldUK
  2. 2.Alfréd Rényi Institute of Mathematics of the Hungarian Academy of SciencesBudapestHungary

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