A universal inductive inference machine

A Universal Inductive Inference Machine

A paradigm of scientific discovery is defined within a first-order logical framework. It is shown that within this paradigm there exists a formal scientist that is Turing computable and universal in the sense that it solves every problem that any scientist can solve. It is also shown that universal scientists exist for no regular logics that extend first order logic and satisfy the Lowenheim-Sk...

Inductive Inference

Probabilistic inductive inference: a survey

Inductive inference is a recursion-theoretic theory of learning, rst developed by E. M. Gold (1967). This paper surveys developments in probabilistic inductive inference. We mainly focus on nite inference of recursive functions, since this simple paradigm has produced the most interesting (and most complex) results.

Fixed Parameter Inductive Inference

We investigate a particular inductive inference problem where we are given as input a finite set of ordered triples of the form (wi, bi, ti) such that wi is a bit string, bi is a single bit, and ti is a positive integer written in unary. A machine M is said to match such a triple if M outputs bi on input wi in at most ti steps. We proceed to investigate the fixed parameter problems where we fix...

Statistics as Inductive Inference

This chapter concerns the relation between statistics and inductive logic. I start by describing induction in formal terms, and I introduce a general notion of probabilistic inductive inference. This provides a setting in which statistical procedures and inductive logics can be captured. Specifically, I discuss three statistical procedures (hypotheses testing, parameter estimation, and Bayesian...