Modelling the US Constitution in HOL
The thesis aims at modelling parts of the US Constitution with higher order logic (HOL) in theorem prover ISABELLE/HOL in order to verify the possibility of a legal dictatorship in the USA. The basis for the argument is a notorious anecdote on how, at his US citizenship hearing, logican Kurt Gödel informed the judge that the US Constitution was in fact faulty and allowed for the erection of a constitutional dictatorship. We shall explore both the argument Gödel might have had in mind when saying this and a verified version of the supposed argument, modelled on the computer.
Before delving into the argument, we give a short overview on the tools used, including an introduction to Isabelle/HOL and the manner in which we are going to use it.
The ensuing section of this work is concerned with Gödel's supposed argument on the Constitution's shortcomings. This also encompasses a quick overview of the Constitution and a more detailed consideration of the articles most relevant to the argument.
After having laid a theoretical foundation, we will devise and implement a HOL model for the argument in the main part of this work. Being mindful of the technical restrictions, we shall choose a suitable logic embedded into Isabelle's HOL-language and map the relevant parts of the Constitution to their equivalents in the proposed logic. Havind succeeded in this, we shall prove that it is possible to build a dictatorship without violating the Constitution, thus verifying Gödel's argument. The main part concludes with a few remarks on what to avoid when modelling a concept with Isabelle/HOL.
The last section will present a few further problematic properties of the US Constitution in addition to the one modelled in the main part. We then name a few questions not yet addressed and conclude the thesis.
For convenience, the terms "US Constitution" and "(the) Constitution shall be used interchangeably.