The Principle of Predicate Exchangeability in Pure Inductive Logic

Abstract

We investigate the Principle of Predicate Exchangeability in the framework of PureInductive Logic.While this principle was known to Rudolf Carnap, who started research in InductiveLogic, the principle has been somewhat neglected in the past.After providing the framework of Pure Inductive Logic, we will show RepresentationTheorems for probability functions satisfying Predicate Exchangeability, filling thegap in the list of Representation Theorems for functions satisfying certain rationalprinciples.We then introduce a new principle, called the Principle of Strong Predicate Exchange-ability, which is weaker than the well-known Principle of Atom Exchangeability, butstronger than Predicate Exchangeability and give examples of functions that satisfythis principle.Finally, we extend the framework of Inductive Logic to Second Order languages, whichallows for increasing a rational agent's expressive strength. We introduce Wilmers'Principle, a rational principle that rational agents might want to adopt in this extendedframework, and give a representation theorem for this principle.

Date of Award	1 Aug 2014
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Jeffrey Paris (Supervisor) & Alena Vencovska (Supervisor)