Most standard results on structure identification in first order theories depend upon the correctness and completeness (in the limit) of the data, which are provided to the learner. These assumption are essential for the reliability of inductive methods and for their limiting success (convergence to the truth). The paper investigates inductive inference from (possibly) incorrect and incomplete data. It is shown that such methods can be reliable not in the sense of truth approximation, but in the sense that the methods (...) converge to "empirically adequate" theories, i.e. theories, which are consistent with all data (past and future) and complete with respect to a given complexity class of L-sentences. Adequate theories of bounded complexity can be inferred uniformly and effectively by polynomial-time learning algorithms. Adequate theories of unbounded complexity can be inferred pointwise by less efficient methods. (shrink)

A comprehensive model for describing various forms of developments in science is defined in precise, set-theoretic terms, and in the spirit of the structuralist approach in the philosophy of science. The model emends previous accounts in centering on single systems in a homogenous way, eliminating notions which essentially refer to sets of systems. This is achieved by eliminating the distinction between theoretical and non-theoretical terms as a primitive, and by introducing the notion of intended links. The force of the model (...) is demonstrated by formally incorporating many of the important, precise meta-theoretic concepts occurring in the literature. (shrink)