This was originally posted at halfbakery.com, where you can see the follow-up comments.
Most democracies have largely secular, rational post-enlightenment systems of government whose power flows neither from gun barrels nor arguments from authority to continue operating. However, because of the advance of technology, the laws these governments pass (and the way they can operate) will continue running into situations that their founders couldn't possibly have anticipated.
Currently many of these problems are solved by court rulings, which establish precedents. These precedents accumulate until there are layers upon layers, not all of them consistent with each other. Laws passed by legislative bodies also can take the form of an inconsistent patchwork that fail to take into account what went before.
By writing a constitution in a logical programming language that generates new laws and automatically checks for internal conflicts, these inefficiencies and inconsistencies can be avoided. Governments would become much truer to the ideal of being made of laws, and not of men.