Carnapian Inductive Logic for Exponential Smoothing

This paper explores the inductive logic associated with exponential smoothing, the most widely used predictive rule that manifests the idea that more recent observations have a stronger influence on predictive probabilities than more remote ones. The main result shows that exponential smoothing can be derived from a set of plausible qualitative invariance assumptions about conditional probabilities. I discuss various aspects of the resulting inductive logic, including its connections to exchangeable processes, to Bayesian predictive inference and kernel methods in machine learning, as well as the philosophy of probabilistic invariance conditions and symmetries.