Questions of Reasoning Under Logical Uncertainty

A logically uncertain reasoner would be able to reason as if they know both a programming language and a program, without knowing what the program outputs. Most practical reasoning involves some logical uncertainty, but no satisfactory theory of reasoning under logical uncertainty yet exists. A better theory of reasoning under logical uncertainty is needed in order to develop the tools necessary to construct highly reliable artificial reasoners. This paper introduces the topic, discusses a number of historical results, and describes a number of open prob-