  Answer set programming is one of the most praised frameworks for declarative
programming in general and non-monotonic reasoning in particular. There has
been many efforts to extend stable model semantics so that answer set programs
can use a more extensive syntax. To such endeavor, the community of
non-monotonic reasoning has introduced extensions such as equilibrium models
and FLP semantics. However, both of these extensions suffer from two problems:
intended models according to such extensions (1) are not guaranteed to be
minimal, and (2) more importantly, may have self-justifications (i.e., the
justification for pertinence of an atom in an intended model may be its own
pertinence). Both of these properties directly violate the spirit of stable
model semantics. Therefore, we believe that we need a new extension of stable
model semantics that guarantees both minimality and being strongly grounded.
  This paper introduces one such extension using two different approaches:
firstly, by extending the goal-reachability interpretation of logic programs to
the full propositional language and, secondly, using derivability in
intuitionistic propositional logic. We show that both these approaches give the
same semantics, that we call the supported semantics. Moreover, using the first
approach, we also extend well-founded semantics to full propositional language.
Furthermore, we discuss how our supported models relate to other existing
semantics for non-monotonic reasoning including the equilibrium models. Last,
but not the least, we discuss the complexity of reasoning about supported
models and show that all interesting reasoning tasks (such as brave/cautious
reasoning) are PSPACE-complete. Therefore, supported model semantics is a much
more expressive semantics then the existing semantics such as equlibrium models
(that have reasoning procedures in $\Delta^P_3$).
