Abstract: One of the most used assumptions in logic programming
and deductive databases is the so-called Closed World Assumption
(CWA), according to which the atoms that cannot be inferred
from the programs are considered to be false (i.e. a pessimistic
assumption). One of the most successful semantics of conventional
logic programs based on the CWA is the well-founded semantics.
However, the CWA is not applicable in all circumstances when
information is handled. That is, the well-founded semantics, if
conventionally defined, would behave inadequately in different cases.
The solution we adopt in this paper is to extend the well-founded
semantics in order for it to be based also on other assumptions. The
basis of (default) negative information in the well-founded semantics
is given by the so-called unfounded sets. We extend this concept
by considering optimistic, pessimistic, skeptical and paraconsistent
assumptions, used to complete missing information from a program.
Our semantics, called extended well-founded semantics, expresses
also imperfect information considered to be missing/incomplete,
uncertain and/or inconsistent, by using bilattices as multivalued
logics. We provide a method of computing the extended well-founded
semantics and show that Kripke-Kleene semantics is captured by
considering a skeptical assumption. We show also that the complexity
of the computation of our semantics is polynomial time.