Pereira and Alferes (1992) introduced a version of well-founded semantics that adheres to the so-called coherence principle which requires that strong negation implies weak negation. We will show later in Sect. 3 how the coherence principle can be introduced in our approach.
Note that for historical reasons we follow the convention that the minimal rules are the preferred ones.
The seminormal form of 133#133 is
where 135#135 is the complement of
. The term seminormal is taken from Reiter (1980).
Pereira and Alferes (1992) argue that each extension of well-founded semantics to two types of negation should satisfy what they call coherence principle: a weakly negated precondition should be considered satisfied whenever the corresponding strongly negated literal is derived. To model this principle in our approach one would have to weaken the notion of
-safeness even further. In the inductive definition, a rule
would have to be considered a member of 151#151 whenever for each weak precondition 152#152 of
154#154, where 155#155 if
is an atom and
In realistic settings one would again use a schema here. In order to keep the example simple we use the relevant instance of the schema directly.
Thu Feb 8 10:26:15 MET 1996