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Showing posts from October, 2005

Skolem's paradox

I was cruising the net looking for information about skolemization when I stumbled on a paradox that I'd never seen before. Skolem's paradox is one of the most astounding paradoxes that I've ever seen. Here are a few links I dug up on the subject: The Löwenheim-Skolem TheoremMOORE ON SKOLEM'S PARADOXReflections on Skolem's Paradox I'm don't totally understand all the implications of the paradox, but I do understand some of them and I find it both fascinating, and in some ways disheartening.

Wish List

I've often had questions that I wanted answers to and didn't know who to ask.  Sometimes the questions are unanswerable unless some mighty alien intelligence were to come and give them to me.  Often times however, they are questions that should in principle be answerable.  Here are some questions from my current wish list.

1. Is it the case that the operational procedures that are used to "prove" queries in logic programming languages are exactly program extraction?  Am I missing something in this picture?

2. The Curry-Howard correspondence gives rise to a simple logic as the type calculus in functional programming languages.  In a language like Haskell this means that you write mostly in the functional programming language and most of logical implications are infered using Hindley-Milner type inference.  If we go to the other extreme we see things like Coq that allow us to do program extraction (extraction of a functional program) from a logical specification.  My q…