The Inductive Logic of Information Systems

TL;DR

This paper develops an inductive logic framework for information systems, focusing on binary hypotheses, where conclusions are more informative than premises, justified by expected information value.

Contribution

It introduces a formal inductive logic for information systems, complete for binary hypotheses and partially applicable to multi-hypotheses systems.

Findings

Complete logic for binary hypotheses

Partial applicability to multi-hypotheses systems

Inferences are justified by expected information value

Abstract

An inductive logic can be formulated in which the elements are not propositions or probability distributions, but information systems. The logic is complete for information systems with binary hypotheses, i.e., it applies to all such systems. It is not complete for information systems with more than two hypotheses, but applies to a subset of such systems. The logic is inductive in that conclusions are more informative than premises. Inferences using the formalism have a strong justification in terms of the expected value of the derived information system.