Logical perspectives on the foundations of probability

We illustrate how a variety of logical methods and techniques provide useful, though currently underappreciated, tools in the foundations and applications of reasoning under uncertainty. The field is vast spanning logic, artificial intelligence, statistics, and decision theory. Rather than (hopelessly) attempting a comprehensive survey, we focus on a handful of telling examples. While most of our attention will be devoted to frameworks in which uncertainty is quantified probabilistically, we will also touch upon generalisations of probability measures of uncertainty, which have attracted a significant interest in the past few decades.

Automated summary

This paper illustrates the usefulness of logical methods and techniques in the foundations and applications of reasoning under uncertainty, which are currently undervalued. The field encompasses logic, artificial intelligence, statistics, and decision theory. Instead of attempting a comprehensive survey, the paper focuses on a few notable examples. While the majority of attention is given to probabilistic frameworks for quantifying uncertainty, the paper also touches upon generalizations of probability measures that have gained significant interest in recent decades.