Predicate Exchangeability and Language Invariance in Pure Inductive Logic

TL;DR

This paper investigates conditions under which probability functions in pure inductive logic that satisfy predicate exchangeability also adhere to unary language invariance, exploring foundational principles of rational belief.

Contribution

It analyzes the relationship between predicate exchangeability and unary language invariance in pure inductive logic, providing conditions linking these principles.

Findings

Predicate exchangeability implies unary language invariance under certain conditions

Characterization of probability functions satisfying both principles

Insights into rational belief principles in inductive logic

Abstract

In Pure Inductive Logic, the rational principle of Predicate Exchangeability states that permuting the predicates in a given language L and replacing each occurrence of a predicate in an L-sentence $\phi$ according to this permutation should not change our belief in the truth of $\phi$. In this paper we study when a probability function w on a purely unary language L satisfying Predicate Exchangeability also satisfies the principle of Unary Language Invariance.