Representation Theorems for Strong Predicate Exchangeability in Pure Inductive Logic

TL;DR

This paper establishes a de Finetti-style representation theorem for probability functions in Pure Inductive Logic that satisfy Strong Predicate Exchangeability and Unary Language Invariance, advancing the theoretical understanding of symmetry principles.

Contribution

It introduces a new representation theorem for probability functions under Strong Predicate Exchangeability, bridging the gap between Predicate and Atom Exchangeability.

Findings

Proves a de Finetti-style representation theorem for these probability functions.

Shows the relationship between Strong Predicate Exchangeability and Unary Language Invariance.

Provides a formal foundation for symmetry principles in Pure Inductive Logic.

Abstract

In Pure Inductive Logic, the principle of Strong Predicate Exchangeability is a rational principle based on symmetry that sits in between the principles of Predicate Exchangeability and Atom Exchangeability. We will show a de Finetti - style representation theorem for probability functions that satisfy this principle in addition to Unary Language Invariance.