Set-theoretic completeness for epistemic and conditional logic

The standard approach to logic in the literature in philosophy and mathemat ics, which has also been adopted in computer science, is to define a langua ge (the syntax), an appropriate class of models together with an interpreta tion of formulas in the language (the semantics), a collection of axioms an d rules of inference characterizing reasoning (the proof theory), and then relate the proof theory to the semantics via soundness and completeness res ults. Here we consider an approach that is more common in the economics lit erature, which works purely at the semantic, set-theoretic level. We provid e set-theoretic completeness results for a number of epistemic and conditio nal logics, and contrast the expressive power of the syntactic and set-theo retic approaches.