DefinePK

Abstract

The family of stable models for a logic program with one negation
was studied by Melvin Fitting. We introduce extended stable model semantics
of logic programs with many negations, which natural extends the notion of stable
model semantics for logic programs with one negation. We use the notion of bilattice
with two ordering which defines the structure of the family of stable models.
The first one is called knowledge ordering, the second one is called degree
of truth. For a vector of valuations in a billatice B, we define
a pseudovaluation and an operator associated to a program .
We also consider the notion of i-model for a program .
For an operator we define a fixed-point iteration. This iteration is applied
to the operator associated to
and produces so-called extended stability operators. When the fixed-point iteration
can be applied by n times, where n is the number of negations, then every fixed
point of the last operator is an extended stable valuation of .