 From qualitative to quantitative probability Early attempts in this direction go back to Finetti (1970 [1974]), striving for a purely qualitative axiomatization of probability theory. A step further towards logical reasoning are various theories of qualitative probability (Kyburg 1994), often based on the assumption that classical quantitative notions of probability are too demanding for real-life agents. In this line of research agents need only reason with partial, comparative probability assessments, rather than having fully specified probabilities for all events. Logical frameworks for qualitative probability include Segerberg (1971), Fagin, Halpern, and Megiddo (1990), and Delgrande and Renne (2015). While differing in detail, all logics in this line have in common that they allow for expressions of the form \(\varphi\preceq\psi\), indicating that \(\psi\) is judged at least as probable at \(\varphi\). Recent frameworks add various additional refinements to this language. Similarly, Heifetz and Mongin (2001) expand the axiomatic analysis of probabilistic beliefs to higher order reasoning, working on probabilistic type space akin to those introduced in  Section 3.7.