  We present a system of relational syllogistic, based on classical
propositional logic, having primitives of the following form:
  Some A are R-related to some B;
  Some A are R-related to all B;
  All A are R-related to some B;
  All A are R-related to all B.
  Such primitives formalize sentences from natural language like `All students
read some textbooks'. Here A and B denote arbitrary sets (of objects), and R
denotes an arbitrary binary relation between objects. The language of the logic
contains only variables denoting sets, determining the class of set terms, and
variables denoting binary relations between objects, determining the class of
relational terms. Both classes of terms are closed under the standard Boolean
operations. The set of relational terms is also closed under taking the
converse of a relation. The results of the paper are the completeness theorem
with respect to the intended semantics and the computational complexity of the
satisfiability problem.
