  The standard approach to logic in the literature in philosophy and
mathematics, which has also been adopted in computer science, is to define a
language (the syntax), an appropriate class of models together with an
interpretation of formulas in the language (the semantics), a collection of
axioms and rules of inference characterizing reasoning (the proof theory), and
then relate the proof theory to the semantics via soundness and completeness
results. Here we consider an approach that is more common in the economics
literature, which works purely at the semantic, set-theoretic level. We provide
set-theoretic completeness results for a number of epistemic and conditional
logics, and contrast the expressive power of the syntactic and set-theoretic
approaches
