Avoiding triviality: Fuzzy implications and conditional events

Abstract

This paper investigates four questions. What are the logical presuppositions underlying classical probability that have a role to play in David Lewis's proof of triviality concerning probabilities of conditionals and conditional probabilities? To what extent and how are they avoided in fuzzy logics when we treat semantic evaluations as the analogues of probability distributions? The introduction into the classical setting of conditional events (or assertions)—as opposed to implications—as a class of objects whose probabilities are equated with conditional probabilities has been the object of much recent investigation. To what extent, if any, can fuzzy logics accommodate the analogues of conditional events? How is triviality avoided in conditional event algebras?