Logic and the Department of Motor Vehicles, Part II

A few years ago, I blogged about the fact that I had to wait on line to renew a non-driver's ID but a driver's license could be renewed by mail:

It's a logical theorem: A and B imply A. In this case, if a card can be used as an ID and the card can be used to drive legally then the card can be used as an ID. The Department of Motor Vehicles disagrees. Apparently, the geniuses at the Department of Motor Vehicles think that a card that can be used to drive legally cannot be used as a plain ID. I'm reminded of tests of the average citizen's understanding of logic. A substantial fraction of the population think “Joe is a computer programmer and a nerd” is more probable than “Joe is a nerd,” even though the first implies the second.

On the other hand, according to Good Math, Bad Math, there is a form of logic in which the regulations make sense. It's called linear logic:

For those who haven't ever seen it before, linear logic is based on the idea of resource consumption. Where the normal propositional or predicate logics that most of us are familiar with are focused around an idea of truth, linear logic is focused on the idea of resource posession and consumption. In standard propositional logic, if you're given the proposition "A", that means that A is true, and you can use the truth of A in as many inferences as you want. In linear logic, if you're given the proposition "A", that means that you possess one instance of A, and you can use it, once, in an inference.

That might mean the regulations aren't completely stupid.

On the other hand, linear logic only applies here if the license is torn up after each use, which I don't think happens that often.