Semantic Information Streams: Toward a Dynamic Theory of Information

Information is typically treated as a static object, evaluated at individual points in time. However, in many real-world processes, information unfolds as a continuous, time-dependent structure.

In this work we introduce the concept of an Information Stream (IS) defined as an ordered sequence of information states evolving over time. We further identify Semantic Information Streams (SIS) as a specific class of such streams, where individual states are interpretable as meaningful entities within a given context.

We propose a minimal set of metrics to characterize semantic streams, including novelty, redundancy, and entropy. These metrics enable parameterization of information streams and allow them to be treated as signals evolving in time.

This perspective shifts the analysis of information from static evaluation to dynamic characterization. In contrast to descriptive approaches to information dynamics, the proposed framework enables parameterized representation of information streams, providing a foundation for applying concepts from dynamical systems and control theory.