We investigate the Principle of Predicate Exchangeability in the framework of Pure Inductive Logic. While this principle was known to Rudolf Carnap, who started research in Inductive Logic, the principle has been somewhat neglected in the past. After providing the framework of Pure Inductive Logic, we will show Representation Theorems for probability functions satisfying Predicate Exchangeability, filling the gap in the list of Representation Theorems for functions satisfying certain rational principles. We then introduce a new principle, called the Principle of Strong Predicate Exchangeability, which is weaker than the well-known Principle of Atom Exchangeability, but stronger than Predicate Exchangeability and give examples of functions that satisfy this principle. Finally, we extend the framework of Inductive Logic to Second Order languages, which allows for increasing a rational agent’s expressive strength. We introduce Wilmers’ Principle, a rational principle that rational agents might want to adopt in this extended framework, and give a representation theorem for this principle.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:603212 |
| Date | January 2014 |
| Creators | Kliess, Malte Sebastian |
| Contributors | Paris, Jeffrey; Vencovska, Alena |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://www.research.manchester.ac.uk/portal/en/theses/the-principle-of-predicate-exchangeability-in-pure-inductive-logic(7483a787-d651-4734-8fdf-eda405fc48a6).html |
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