Hi, (01)
John's point about how approximate solutions to certain NPcomplete
problems can sometimes be computed much more cheaply than the globally
optimal solution made me wonder: (02)
Is there an example of or counterpart to this in logic? (03)
I usually think of logic (at least the nonfuzzy logics) to be rather
rigid and not amenable to approximation. (04)
The closest thing I can think of to this phenomenon (based on recent
implementation experience) is that among all solutions to a given
disjunctive logic programs, often some are far cheaper to discover than
others. In fact, some simple problems based on PSL (Process
Specification Language) have shown a behavior in which, out of N total
solutions, the first N  1 or 2 solutions come very quickly and the
last one or two take 100 or 1000 times as many inferences to discover.
(Of course, this is for a few problems computed with a particular
implementation of DLP under a particular search heuristic and so is far
from a universal observation.) (05)
Anyway, how generally amenable is logical inference to approximation
techniques? (06)
Randall Schulz (07)
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