0000000000470668
AUTHOR
Carl H. Smith
Learning formulae from elementary facts
Since the seminal paper by E.M. Gold [Gol67] the computational learning theory community has been presuming that the main problem in the learning theory on the recursion-theoretical level is to restore a grammar from samples of language or a program from its sample computations. However scientists in physics and biology have become accustomed to looking for interesting assertions rather than for a universal theory explaining everything.
Learning with belief levels
AbstractWe study learning of predicate logics formulas from “elementary facts,” i.e. from the values of the predicates in the given model. Several models of learning are considered, but most of our attention is paid to learning with belief levels. We propose an axiom system which describes what we consider to be a human scientist's natural behavior when trying to explore these elementary facts. It is proved that no such system can be complete. However we believe that our axiom system is “practically” complete. Theorems presented in the paper in some sense confirm our hypothesis.