A logic using three truth values (true, false, undefined) is described
together with its Horn clause subset and a procedural interpretation.
The resulting logic programming language allows clauses to affirm
both positive and negative information and can test whether a goal
is definitely false or is just not provably true (standard negation
by failure) as well as other possibilities including whether it is
unknown (cannot be proven either true or false). The major theoretical
results characterizing classical logic programs can be carried over to this
context, including the equivalence of a programs answer set with the minimal
Herbrand universe and least fixed point semantics as well as the
correctness and completeness of SLD-resolution. The logic can be
easily implemented within existing Prolog interpreters.
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