Scientific knowledge systems function as effective and specialized app
aratus for formulating, analyzing and solving scientific problems. In
science, problems become internal parts of the knowledge systems; thus
they acquire new forms and properties in comparison with common-sense
problems. Definite theoretical structures connected with problems and
questions appear in the theory. Among them are erotetic expressions a
nd languages, calculi and algebras of problems. On the basis of the st
ructure-nominative reconstruction of a theory, the unified treatment o
f these structures is given. Methods of the theory of named sets are u
sed in the logical analysis of problems and their systems. As a conseq
uence a new formalized model of the problem part of theory is construc
ted.