Vicious Circle Principle and Formation of Sets in ASP Based Languages
  The paper continues the investigation of Poincare and Russel's Vicious Circle
Principle (VCP) in the context of the design of logic programming languages
with sets. We expand previously introduced language Alog with aggregates by
allowing infinite sets and several additional set related constructs useful for
knowledge representation and teaching. In addition, we propose an alternative
formalization of the original VCP and incorporate it into the semantics of new
language, Slog+, which allows more liberal construction of sets and their use
in programming rules. We show that, for programs without disjunction and
infinite sets, the formal semantics of aggregates in Slog+ coincides with that
of several other known languages. Their intuitive and formal semantics,
however, are based on quite different ideas and seem to be more involved than
that of Slog+.
