Inductive reasoning

Our aim is to explain a general theory of inductive reasoning which is close enough to the concerns of language studies. In this setup , the optimal prediction rate is assigned to the hypothesis considered most likely by a prior-free form of Bayesian inference. In terms of practical applications a most attractive form of this approach is embodied by the so-called minimum description length (MDL) principle. There, the most likely hypothesis is the one which minimizes the sum of the length of the description of the hypothesis and the length of the description of the data relative to the hypothesis. This theory is solidly based on a provably ideal method of inference using Kolmogorov complexity. We give references to several applications. Similar approaches should work for computational learning of features of language. The genesis of this work is not rooted in traditional approaches to artiicial intelligence (AI), but rather in new exciting general learning theories which have developed out from the computational complexity theory 21, 20], statistics and descriptional (Kolmogorov) complexity 15]. These new theories have received One the other hand, the design of real learning systems seemed to be dominated by ad hoc trial-and-error methods. It is commonly accepted that all learning involves compression of experimental data in a compact`theory' , `hypothesis', or`model' of the phenomenon under investigation. In 11, 12] the authors analysed the theory of such approaches related to shortest eeective description length (Kolmogorov complexity). The question arises whether these theoretical insights can be directly applied to real