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\section{
Checking the Consistency of Laws}

Despite the constant checks at all levels of the court system,
the immensity and cumulative nature of the U.S. legal code means
not all laws are necessarily consistent with one another.  
The problem is compounded with the addition of the legal codes
of the fifty states, which may present other inconsistencies
with the federal code.  Identifying these inconsistencies is, at 
its most basic, an enormous search problem.  

The storage required is many gigabytes.  The federal legal code
occupies about 180,000 printed pages.  The code of federal regulations
is substantially larger.  A typical state code can be over
20,000 printed pages.  An electronic version of these codes
in their entireties would require tens of gigabytes of storage.  
Because the codes include a substantial amount of annotation,
the statutes could be encoded alone in substantially less space.

Several mechanisms are possible for checking the consistency
of encoded laws.  One small prototype study used techniques of logic 
programming (automated theorem proving) to check the consistency of 
British tort law.  A different approach would be to use a 
semantic codification of the statutes.  Consistencies could
be identified geometrically via techniques similar to those used in
lexical semantic indexing.  (The laws are cast as a vector space
and all laws within a certain distance of a given law are
checked (automatically or by a person)  for consistency with the
given law.  The distances are determined by computing the 
cosines between the vectors representing the laws.)   A neural
net data base could also be used to determine the related vectors.

In any incarnation, this computation requires the codification
of the laws in a way appropriate to the methods used for consistency
checking.   Given the size of the database, this process is
practical only if automated.  The consistency check requires the 
comparison of each statute with all others.   That is, if $n$ laws are 
to be checked, O(n^2) pairs of laws must be compared.  Identifying
the related laws is a likely to be a tractable problem, requiring,
for example, a dot product of each pair of law vectors.   Determining
consistency between those vectors would be substantially more
compute intensive.  If checking the consistency of a pair of
vectors required $10^4$ operations, a database of $10^5$ codified laws could
be checked for consistency in about $10^14$ operations.
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