Chris, (01)
A few points of clarification: (02)
JFS>> I noticed that in the Q/A section of Pat's talk, somebody said
>> that CL is too expressive -- therefore, it is inefficient.
>>
>> But that question is hopelessly confused. (03)
CM> Agreed. (04)
JFS>> It is based on the assumption that there is *one and only one*
>> method of using or reasoning with any given logic. But that
>> assumption does not hold for *any* natural language, programming
>> language, query language, or, indeed, any version of logic. (05)
CM> It's not clear to me that that is necessarily being assumed.
> Another possibility is that the questioner believes that
> representation languages should be *paternalistic* -- that is,
> they should prevent users from even posing questions that are
> undecidable. (06)
I agree that the person who made that statement may have had
different motivations or perhaps multiple motivations. (07)
CM> It seems to me that it makes sense to have such languages for
> a certain class of user who is not wise in the ways of computational
> complexity. (08)
I think we agree on the issues, but there are many different ways
of protecting naive users: (09)
1. Paternalistic, as above. (010)
2. Collaborative: Provide a very general language that is
supported by a large number of different engines for different
subsets and purposes. When a given problem is stated, the
system selects an appropriate processor (which can usually be
done on purely syntactic grounds before any detailed computation
is attempted). If the problem falls into one of the more
difficult complexity classes, warn the user and ask for advice. (011)
3. Supportive: Provide a large set of development tools, which
guide the user in a variety of different ways of using the
system for an open-ended range of tasks and user skills. (012)
Methods #2 and #3 or some combination can provide all the benefits
of the paternalistic approach without imposing any draconian or
Procrustean constraints on what the user is allowed to do. (013)
JFS>> For database queries and constraints, SQL supports full FOL, but
>> even the worst case examples can be evaluated in polynomial time... (014)
CM> I am probably not understanding the claim, but how is this possible
> if SQL supports full FOL, in which we can easily express problems that
> can be solved, if at all, in at best exponential time? (015)
SQL evaluates the truth value of a given FOL statement in terms of
a fixed model (i.e., the current state of the database). That takes
polynomial time. SQL never evaluates a statement in terms of all
possible models, which might require exponential time or even be
undecidable. (016)
The paternalistic approach assumes that all users are trying to
prove a theorem that is valid for all possible models. But most
people who ask a question are only interested in a specific model,
such as the current DB. (017)
John (018)
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